$X$ and $Y$ are normally distributed independent random variables with mean zero and variance 1, so $X, Y \sim N(0, 1)$.
I'm trying to calculated the conditional expectation: $ \mathbb{E}(\exp(X-Y) \mid X+Y)$.
I've tried to write the expectation as $\exp(X+Y-2Y)$, however since $-2Y$ is not independent of $X+Y$ this clearly gives an incorrect solution. How can this expectation be calculated?