diff --git a/doc/source/whatsnew/v0.23.0.txt b/doc/source/whatsnew/v0.23.0.txt
index 6407a33c442d0..0cd07de2e456d 100644
--- a/doc/source/whatsnew/v0.23.0.txt
+++ b/doc/source/whatsnew/v0.23.0.txt
@@ -208,6 +208,7 @@ Other API Changes
 - In :func:`read_excel`, the ``comment`` argument is now exposed as a named parameter (:issue:`18735`)
 - Rearranged the order of keyword arguments in :func:`read_excel()` to align with :func:`read_csv()` (:issue:`16672`)
 - The options ``html.border`` and ``mode.use_inf_as_null`` were deprecated in prior versions, these will now show ``FutureWarning`` rather than a ``DeprecationWarning`` (:issue:`19003`)
+- Subtracting ``NaT`` from a :class:`Series` with ``dtype='datetime64[ns]'`` returns a ``Series`` with ``dtype='timedelta64[ns]'`` instead of ``dtype='datetime64[ns]'``(:issue:`18808`)
 
 .. _whatsnew_0230.deprecations:
 
diff --git a/pandas/core/ops.py b/pandas/core/ops.py
index faac8ab312d6b..18659898ae442 100644
--- a/pandas/core/ops.py
+++ b/pandas/core/ops.py
@@ -407,8 +407,12 @@ def _validate_datetime(self, lvalues, rvalues, name):
 
             # if tz's must be equal (same or None)
             if getattr(lvalues, 'tz', None) != getattr(rvalues, 'tz', None):
-                raise ValueError("Incompatible tz's on datetime subtraction "
-                                 "ops")
+                if len(rvalues) == 1 and isna(rvalues).all():
+                    # NaT gets a pass
+                    pass
+                else:
+                    raise ValueError("Incompatible tz's on datetime "
+                                     "subtraction ops", rvalues)
 
         else:
             raise TypeError('cannot operate on a series without a rhs '
@@ -505,11 +509,20 @@ def _convert_to_array(self, values, name=None, other=None):
         inferred_type = lib.infer_dtype(values)
         if (inferred_type in ('datetime64', 'datetime', 'date', 'time') or
                 is_datetimetz(inferred_type)):
+
+            if ovalues is pd.NaT and name == '__sub__':
+                # Note: This can only occur when `values` represents `right`
+                # i.e. `other`.
+                if other.dtype == 'timedelta64[ns]':
+                    values = np.array([iNaT], dtype='timedelta64[ns]')
+                else:
+                    values = np.array([iNaT], dtype='datetime64[ns]')
+
             # if we have a other of timedelta, but use pd.NaT here we
             # we are in the wrong path
-            if (supplied_dtype is None and other is not None and
-                (other.dtype in ('timedelta64[ns]', 'datetime64[ns]')) and
-                    isna(values).all()):
+            elif (supplied_dtype is None and other is not None and
+                  (other.dtype in ('timedelta64[ns]', 'datetime64[ns]')) and
+                  isna(values).all()):
                 values = np.empty(values.shape, dtype='timedelta64[ns]')
                 values[:] = iNaT
 
diff --git a/pandas/tests/series/test_operators.py b/pandas/tests/series/test_operators.py
index ce4e388bc6f39..019476c467166 100644
--- a/pandas/tests/series/test_operators.py
+++ b/pandas/tests/series/test_operators.py
@@ -960,6 +960,13 @@ def test_timedelta64_ops_nat(self):
         assert_series_equal(timedelta_series / nan,
                             nat_series_dtype_timedelta)
 
+    def test_td64_sub_NaT(self):
+        # GH#18808
+        ser = Series([NaT, Timedelta('1s')])
+        res = ser - NaT
+        expected = Series([NaT, NaT], dtype='timedelta64[ns]')
+        tm.assert_series_equal(res, expected)
+
     @pytest.mark.parametrize('scalar_td', [timedelta(minutes=5, seconds=4),
                                            Timedelta(minutes=5, seconds=4),
                                            Timedelta('5m4s').to_timedelta64()])
@@ -1224,13 +1231,10 @@ def test_datetime64_ops_nat(self):
         single_nat_dtype_datetime = Series([NaT], dtype='datetime64[ns]')
 
         # subtraction
-        assert_series_equal(datetime_series - NaT, nat_series_dtype_timestamp)
         assert_series_equal(-NaT + datetime_series, nat_series_dtype_timestamp)
         with pytest.raises(TypeError):
             -single_nat_dtype_datetime + datetime_series
 
-        assert_series_equal(nat_series_dtype_timestamp - NaT,
-                            nat_series_dtype_timestamp)
         assert_series_equal(-NaT + nat_series_dtype_timestamp,
                             nat_series_dtype_timestamp)
         with pytest.raises(TypeError):
@@ -1263,6 +1267,20 @@ def test_datetime64_ops_nat(self):
         with pytest.raises(TypeError):
             nat_series_dtype_timestamp / 1
 
+    def test_dt64_sub_NaT(self):
+        # GH#18808
+        dti = pd.DatetimeIndex([pd.NaT, pd.Timestamp('19900315')])
+        ser = pd.Series(dti)
+        res = ser - pd.NaT
+        expected = pd.Series([pd.NaT, pd.NaT], dtype='timedelta64[ns]')
+        tm.assert_series_equal(res, expected)
+
+        dti_tz = dti.tz_localize('Asia/Tokyo')
+        ser_tz = pd.Series(dti_tz)
+        res = ser_tz - pd.NaT
+        expected = pd.Series([pd.NaT, pd.NaT], dtype='timedelta64[ns]')
+        tm.assert_series_equal(res, expected)
+
 
 class TestSeriesOperators(TestData):
     def test_op_method(self):