diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index 68736935ed36d..20ca176f4a456 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -506,7 +506,7 @@ def asi8(self):
         return None
 
     @classmethod
-    def _simple_new(cls, values, name=None, dtype=None, **kwargs):
+    def _simple_new(cls, values, name=None, dtype=None):
         """
         We require that we have a dtype compat for the values. If we are passed
         a non-dtype compat, then coerce using the constructor.
@@ -528,8 +528,7 @@ def _simple_new(cls, values, name=None, dtype=None, **kwargs):
         # we actually set this value too.
         result._index_data = values
         result.name = name
-        for k, v in kwargs.items():
-            setattr(result, k, v)
+
         return result._reset_identity()
 
     @cache_readonly
@@ -2673,7 +2672,7 @@ def difference(self, other, sort=None):
             except TypeError:
                 pass
 
-        return this._shallow_copy(the_diff, name=result_name, freq=None)
+        return this._shallow_copy(the_diff, name=result_name)
 
     def symmetric_difference(self, other, result_name=None, sort=None):
         """
diff --git a/pandas/core/indexes/datetimes.py b/pandas/core/indexes/datetimes.py
index 4a3ee57084a8a..e19ebf17a1b98 100644
--- a/pandas/core/indexes/datetimes.py
+++ b/pandas/core/indexes/datetimes.py
@@ -464,6 +464,12 @@ def _convert_for_op(self, value):
             return _to_M8(value)
         raise ValueError("Passed item and index have different timezone")
 
+    @Appender(Index.difference.__doc__)
+    def difference(self, other, sort=None):
+        new_idx = super().difference(other, sort=sort)
+        new_idx.freq = None
+        return new_idx
+
     # --------------------------------------------------------------------
     # Rendering Methods
 
diff --git a/pandas/core/indexes/range.py b/pandas/core/indexes/range.py
index 962ba8cc00557..0fe0fe5a426ae 100644
--- a/pandas/core/indexes/range.py
+++ b/pandas/core/indexes/range.py
@@ -146,7 +146,7 @@ def from_range(cls, data, name=None, dtype=None):
         return cls._simple_new(data, dtype=dtype, name=name)
 
     @classmethod
-    def _simple_new(cls, values, name=None, dtype=None, **kwargs):
+    def _simple_new(cls, values, name=None, dtype=None):
         result = object.__new__(cls)
 
         # handle passed None, non-integers
@@ -154,13 +154,10 @@ def _simple_new(cls, values, name=None, dtype=None, **kwargs):
             # empty
             values = range(0, 0, 1)
         elif not isinstance(values, range):
-            return Index(values, dtype=dtype, name=name, **kwargs)
+            return Index(values, dtype=dtype, name=name)
 
         result._range = values
-
         result.name = name
-        for k, v in kwargs.items():
-            setattr(result, k, v)
 
         result._reset_identity()
         return result
diff --git a/pandas/core/indexes/timedeltas.py b/pandas/core/indexes/timedeltas.py
index 8114b4a772f28..6caac43af163b 100644
--- a/pandas/core/indexes/timedeltas.py
+++ b/pandas/core/indexes/timedeltas.py
@@ -406,6 +406,12 @@ def intersection(self, other, sort=False):
         """
         return super().intersection(other, sort=sort)
 
+    @Appender(Index.difference.__doc__)
+    def difference(self, other, sort=None):
+        new_idx = super().difference(other, sort=sort)
+        new_idx.freq = None
+        return new_idx
+
     def _wrap_joined_index(self, joined, other):
         name = get_op_result_name(self, other)
         if (