diff --git a/Tests/test_image_point.py b/Tests/test_image_point.py
index 428ad116b3d..157ecb120f0 100644
--- a/Tests/test_image_point.py
+++ b/Tests/test_image_point.py
@@ -1,5 +1,7 @@
 import pytest
 
+from PIL import Image
+
 from .helper import assert_image_equal, hopper
 
 
@@ -17,11 +19,24 @@ def test_sanity():
         im.point(list(range(256)))
     im.point(lambda x: x * 1)
     im.point(lambda x: x + 1)
+    im.point(lambda x: x - 1)
     im.point(lambda x: x * 1 + 1)
+    im.point(lambda x: 0.1 + 0.2 * x)
+    im.point(lambda x: -x)
+    im.point(lambda x: x - 0.5)
+    im.point(lambda x: 1 - x / 2)
+    im.point(lambda x: (2 + x) / 3)
+    im.point(lambda x: 0.5)
+    im.point(lambda x: x / 1)
+    im.point(lambda x: x + x)
+    with pytest.raises(TypeError):
+        im.point(lambda x: x * x)
+    with pytest.raises(TypeError):
+        im.point(lambda x: x / x)
     with pytest.raises(TypeError):
-        im.point(lambda x: x - 1)
+        im.point(lambda x: 1 / x)
     with pytest.raises(TypeError):
-        im.point(lambda x: x / 1)
+        im.point(lambda x: x // 2)
 
 
 def test_16bit_lut():
@@ -47,3 +62,8 @@ def test_f_mode():
     im = hopper("F")
     with pytest.raises(ValueError):
         im.point(None)
+
+
+def test_coerce_e_deprecation():
+    with pytest.warns(DeprecationWarning):
+        assert Image.coerce_e(2).data == 2
diff --git a/docs/deprecations.rst b/docs/deprecations.rst
index ad030acd071..8c5b8a748d7 100644
--- a/docs/deprecations.rst
+++ b/docs/deprecations.rst
@@ -170,6 +170,14 @@ in Pillow 10 (2023-07-01). Upgrade to
 `PyQt6 <https://www.riverbankcomputing.com/static/Docs/PyQt6/>`_ or
 `PySide6 <https://doc.qt.io/qtforpython/>`_ instead.
 
+Image.coerce_e
+~~~~~~~~~~~~~~
+
+.. deprecated:: 9.2.0
+
+This undocumented method has been deprecated and will be removed in Pillow 10
+(2023-07-01).
+
 Removed features
 ----------------
 
diff --git a/docs/releasenotes/9.2.0.rst b/docs/releasenotes/9.2.0.rst
index c38944b10e9..db051d1881f 100644
--- a/docs/releasenotes/9.2.0.rst
+++ b/docs/releasenotes/9.2.0.rst
@@ -31,6 +31,14 @@ FreeTypeFont.getmask2 fill parameter
 The undocumented ``fill`` parameter of :py:meth:`.FreeTypeFont.getmask2`
 has been deprecated and will be removed in Pillow 10 (2023-07-01).
 
+Image.coerce_e
+~~~~~~~~~~~~~~
+
+.. deprecated:: 9.2.0
+
+This undocumented method has been deprecated and will be removed in Pillow 10
+(2023-07-01).
+
 API Changes
 ===========
 
diff --git a/src/PIL/Image.py b/src/PIL/Image.py
index fead48b29d9..4ac4fda26b5 100644
--- a/src/PIL/Image.py
+++ b/src/PIL/Image.py
@@ -29,7 +29,6 @@
 import io
 import logging
 import math
-import numbers
 import os
 import re
 import struct
@@ -432,44 +431,50 @@ def _getencoder(mode, encoder_name, args, extra=()):
 
 
 def coerce_e(value):
-    return value if isinstance(value, _E) else _E(value)
+    deprecate("coerce_e", 10)
+    return value if isinstance(value, _E) else _E(1, value)
 
 
+# _E(scale, offset) represents the affine transformation scale * x + offset.
+# The "data" field is named for compatibility with the old implementation,
+# and should be renamed once coerce_e is removed.
 class _E:
-    def __init__(self, data):
+    def __init__(self, scale, data):
+        self.scale = scale
         self.data = data
 
+    def __neg__(self):
+        return _E(-self.scale, -self.data)
+
     def __add__(self, other):
-        return _E((self.data, "__add__", coerce_e(other).data))
+        if isinstance(other, _E):
+            return _E(self.scale + other.scale, self.data + other.data)
+        return _E(self.scale, self.data + other)
+
+    __radd__ = __add__
+
+    def __sub__(self, other):
+        return self + -other
+
+    def __rsub__(self, other):
+        return other + -self
 
     def __mul__(self, other):
-        return _E((self.data, "__mul__", coerce_e(other).data))
+        if isinstance(other, _E):
+            return NotImplemented
+        return _E(self.scale * other, self.data * other)
+
+    __rmul__ = __mul__
+
+    def __truediv__(self, other):
+        if isinstance(other, _E):
+            return NotImplemented
+        return _E(self.scale / other, self.data / other)
 
 
 def _getscaleoffset(expr):
-    stub = ["stub"]
-    data = expr(_E(stub)).data
-    try:
-        (a, b, c) = data  # simplified syntax
-        if a is stub and b == "__mul__" and isinstance(c, numbers.Number):
-            return c, 0.0
-        if a is stub and b == "__add__" and isinstance(c, numbers.Number):
-            return 1.0, c
-    except TypeError:
-        pass
-    try:
-        ((a, b, c), d, e) = data  # full syntax
-        if (
-            a is stub
-            and b == "__mul__"
-            and isinstance(c, numbers.Number)
-            and d == "__add__"
-            and isinstance(e, numbers.Number)
-        ):
-            return c, e
-    except TypeError:
-        pass
-    raise ValueError("illegal expression")
+    a = expr(_E(1, 0))
+    return (a.scale, a.data) if isinstance(a, _E) else (0, a)
 
 
 # --------------------------------------------------------------------