How to get a part's CFrame offset?

With CFrame, in order to get a part to move in a certain direction based on it's rotation, I found that I can do CFrame(position)*CFrame(offset) but is there a way to get the offset of the part based on the original position?

Assuming position, offset and newPosition are CFrame values:

position * offset = newPosition -- The formula you stated on your post

From that formula, we get:

offset = position:inverse() * newPosition