Calculating the expectation of random exponentioal function using correlation information

Question

Let us assume that the two random variable $X$ and $Y$ are uniformly distributed in $[0,2\pi)$. In addition, the correlation ratio between them is defiend by $\rho$, i.e., $E[XY^*]=\rho$. In this case, can we calculate the following expectation? $$ \begin{align} E[e^{jX-jY}] \end{align} $$ by using $\rho$ information.

Thanks in advance.