Q:

Obtain x from $\exp(-x) \cdot x=y$

$$\exp(-x)  \cdot x=y$$
I want to obtain $x$ from this equation ($x=f(y)$). $x$ and $y$ are positive. I've spent now some time on it and I don't know how to do this. I've tried to use logarithms here, but I can't get a single $x$. 
Is this a difficult equation or did I forget about an easy method to solve it?

A:

This is a trascendental equation, so you cannot explicitly solve for $x$ unless you know something about the Lambert W function.
Cheers!
Edit: in Mathematica this is noted as the "ProductLog" function.

