How can this exponential equation be computed

Question

Is there a mathematical way to solve such equations, besides try and error of course?

$e^{-x} = 1-x/5$

Answer 1

The solution is

$$ x = W(-5e^{-5})+5 $$

besides the solution $ x=0$.

Note: Lambert $W$ function is the solution of the equation

$$ W(t) e^{W(t)} = t. $$