In general, how do you solve for X-Y?

e.g X and Y have p.d.f $\displaystyle f(x)=3x^2$ 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.

any idea?