you can easily get the pdf of -Y, with the region that is different. You can then use the convolution or the transform of variables method.
In general, how do you solve for X-Y?
e.g X and Y have p.d.f for 0<x<1
I know how to solve for X+Y
but for X-Y, C.D.F is effectively the region above a line Y=X-Z bounded by the square 0 to 1.
I think I am stuck with a non standard multiple integral from top left to right bottom.