If $a$ is the solution of the equation $$xe^x=e^2$$
If $b$ is the solution of the equation $$x\ln x=e^2$$

Then what is $ab$?

I know the answer is $e^2$, using the symmetrical property of $\frac{e^2}{x}$, $e^x$, and $\ln x$

But how can I do it algebraically?