Haven't done this in a while, so I just looked on wikipedia. This is what it said (for expected value):
Expected value - Wikipedia, the free encyclopedia
result is valid even if X is not statistically independent of Y.
So in your case E(Y - X) = E(Y) - E(X).
To find your V(Y-X), you'll need to use the following property:
Variance - Wikipedia, the free encyclopedia
since in your case X and Y are not independent, their covariance is not 0.