A friend posed an interesting problem to me, which I've not been able to solve.

You have two pictures of elements A and B

The first picture has only element A

The second picture Has element B on top of Element A.

We're trying to find a way to extract just element B.  But as the images overlap, this is proving problematic. My first thought was to make a layer mask from A, and apply it inverted to B, but this results in a chunk going missing from B. Obviously, this could be done with lots of manual work selecting the right pixels, but that seems tedious, and something tells me there must be an easier way.

Element a is in exactly the same place in both pictures. So I'm wondering if there's any way to remove common pixels over two layers. Does anyone have any idea?

to clarify, we don't actually have any application for this, but are merely trying to find some technique that can be applied to this. I can create visual aids if it would help explain what I mean.