$X$ and $Y$ are two independent normally distributed random variables with means $\mu_X$, $\mu_Y$ and variances $\sigma_X$, $\sigma_Y$. I'm taking pairwise samples and am trying to calculate the expected values of $X$ and $Y$ for all sample pairs with $X>Y$.
I know the difference $X-Y$ for all $X>Y$ is a truncated normal distribution, so I can calculate the expected difference $E(X-Y\,|\,X-Y>0)$, but I have no clue how to get to the individual values.