Is the function $y=xe^x$ invertible? I'm wondering if the equation $re^r=se^s$ has any answer. If there is any answer,and $r=-1+v,s=-1-v$ in which $v$ is a positive real number,what can we say about $v$?
Thank you in advance.

A straightforward solution is 
$$ r=s $$
for whatever parametrization. Other solution involves Lambert function $W$
$$ r + \log r =  s + \log s$$ 
