How to solve $a 2^x - x = b$?

Question

I need to solve $a 2^x - x = b$ for $x$ where $a$ and $b$ are parameters. Does it have closed form solution? I need to substitute $x$ in another system of equations in Mathematica.

Answer 1

$$x = -{\frac {{\rm W} \left(-\ln \left( 2 \right) a{2}^{-b}\right)}{\ln \left( 2 \right) }}-b$$ where $\rm W$ is any branch of the Lambert W function (ProductLog in Mathematica).

But if you have Mathematica, why didn't you ask Mathematica to solve it?