diff --git a/pandas/core/arrays/datetimelike.py b/pandas/core/arrays/datetimelike.py
index 71f834e0f4e01..848d2f879fbf2 100644
--- a/pandas/core/arrays/datetimelike.py
+++ b/pandas/core/arrays/datetimelike.py
@@ -36,6 +36,7 @@
     Period,
     Resolution,
     Tick,
+    Timedelta,
     Timestamp,
     astype_overflowsafe,
     delta_to_nanoseconds,
@@ -1122,7 +1123,7 @@ def _get_i8_values_and_mask(
         if isinstance(other, Period):
             i8values = other.ordinal
             mask = None
-        elif isinstance(other, Timestamp):
+        elif isinstance(other, (Timestamp, Timedelta)):
             i8values = other.value
             mask = None
         else:
@@ -1203,33 +1204,12 @@ def _sub_datetimelike_scalar(self, other: datetime | np.datetime64):
         self = cast("DatetimeArray", self)
         # subtract a datetime from myself, yielding a ndarray[timedelta64[ns]]
 
-        # error: Non-overlapping identity check (left operand type: "Union[datetime,
-        # datetime64]", right operand type: "NaTType")  [comparison-overlap]
-        assert other is not NaT  # type: ignore[comparison-overlap]
-        other = Timestamp(other)
-        # error: Non-overlapping identity check (left operand type: "Timestamp",
-        # right operand type: "NaTType")
-        if other is NaT:  # type: ignore[comparison-overlap]
+        if isna(other):
+            # i.e. np.datetime64("NaT")
             return self - NaT
 
-        try:
-            self._assert_tzawareness_compat(other)
-        except TypeError as err:
-            new_message = str(err).replace("compare", "subtract")
-            raise type(err)(new_message) from err
-
-        i8 = self.asi8
-        result = checked_add_with_arr(i8, -other.value, arr_mask=self._isnan)
-        res_m8 = result.view(f"timedelta64[{self._unit}]")
-
-        new_freq = None
-        if isinstance(self.freq, Tick):
-            # adding a scalar preserves freq
-            new_freq = self.freq
-
-        from pandas.core.arrays import TimedeltaArray
-
-        return TimedeltaArray._simple_new(res_m8, dtype=res_m8.dtype, freq=new_freq)
+        other = Timestamp(other)
+        return self._sub_datetimelike(other)
 
     @final
     def _sub_datetime_arraylike(self, other):
@@ -1241,6 +1221,13 @@ def _sub_datetime_arraylike(self, other):
 
         self = cast("DatetimeArray", self)
         other = ensure_wrapped_if_datetimelike(other)
+        return self._sub_datetimelike(other)
+
+    @final
+    def _sub_datetimelike(self, other: Timestamp | DatetimeArray) -> TimedeltaArray:
+        self = cast("DatetimeArray", self)
+
+        from pandas.core.arrays import TimedeltaArray
 
         try:
             self._assert_tzawareness_compat(other)
@@ -1248,12 +1235,14 @@ def _sub_datetime_arraylike(self, other):
             new_message = str(err).replace("compare", "subtract")
             raise type(err)(new_message) from err
 
-        self_i8 = self.asi8
-        other_i8 = other.asi8
-        new_values = checked_add_with_arr(
-            self_i8, -other_i8, arr_mask=self._isnan, b_mask=other._isnan
+        other_i8, o_mask = self._get_i8_values_and_mask(other)
+        res_values = checked_add_with_arr(
+            self.asi8, -other_i8, arr_mask=self._isnan, b_mask=o_mask
         )
-        return new_values.view("timedelta64[ns]")
+        res_m8 = res_values.view(f"timedelta64[{self._unit}]")
+
+        new_freq = self._get_arithmetic_result_freq(other)
+        return TimedeltaArray._simple_new(res_m8, dtype=res_m8.dtype, freq=new_freq)
 
     @final
     def _sub_period(self, other: Period) -> npt.NDArray[np.object_]:
@@ -1289,24 +1278,15 @@ def _add_timedeltalike_scalar(self, other):
         Same type as self
         """
         if isna(other):
-            # i.e np.timedelta64("NaT"), not recognized by delta_to_nanoseconds
+            # i.e np.timedelta64("NaT")
             new_values = np.empty(self.shape, dtype="i8").view(self._ndarray.dtype)
             new_values.fill(iNaT)
             return type(self)._simple_new(new_values, dtype=self.dtype)
 
         # PeriodArray overrides, so we only get here with DTA/TDA
         self = cast("DatetimeArray | TimedeltaArray", self)
-        inc = delta_to_nanoseconds(other, reso=self._reso)
-
-        new_values = checked_add_with_arr(self.asi8, inc, arr_mask=self._isnan)
-        new_values = new_values.view(self._ndarray.dtype)
-
-        new_freq = None
-        if isinstance(self.freq, Tick) or is_period_dtype(self.dtype):
-            # adding a scalar preserves freq
-            new_freq = self.freq
-
-        return type(self)._simple_new(new_values, dtype=self.dtype, freq=new_freq)
+        other = Timedelta(other)._as_unit(self._unit)
+        return self._add_timedeltalike(other)
 
     def _add_timedelta_arraylike(
         self, other: TimedeltaArray | npt.NDArray[np.timedelta64]
@@ -1334,13 +1314,21 @@ def _add_timedelta_arraylike(
             else:
                 other = other._as_unit(self._unit)
 
-        self_i8 = self.asi8
-        other_i8 = other.asi8
+        return self._add_timedeltalike(other)
+
+    @final
+    def _add_timedeltalike(self, other: Timedelta | TimedeltaArray):
+        self = cast("DatetimeArray | TimedeltaArray", self)
+
+        other_i8, o_mask = self._get_i8_values_and_mask(other)
         new_values = checked_add_with_arr(
-            self_i8, other_i8, arr_mask=self._isnan, b_mask=other._isnan
+            self.asi8, other_i8, arr_mask=self._isnan, b_mask=o_mask
         )
         res_values = new_values.view(self._ndarray.dtype)
-        return type(self)._simple_new(res_values, dtype=self.dtype)
+
+        new_freq = self._get_arithmetic_result_freq(other)
+
+        return type(self)._simple_new(res_values, dtype=self.dtype, freq=new_freq)
 
     @final
     def _add_nat(self):