I want to solve the equation for $x$
$a((x-a)e^{2x/a}+x+a)-z=0$
Conditions on $a$ and $z$ are: $a,z>0$ and both real.
I made some research but couldn't find a lot. Maybe something with the Lambert W function?
In general, I'm interested in solutions of equations of the form
$a=xe^x+bx$