How do I solve for $w$ when it's on both sides and nested within the equation?

Question

I started with the following formula which I've confirmed works:

$$e = aw - b(1 - w)$$

I'm trying to solve for $w$ and this is as far as I got.

$$ w = \frac{e + b(1 - w)}{a}$$

Answer 1

We have $$e = aw - b(1 - w)=aw-b+bw=(a+b)w-b$$ so $$b+e=(a+b)w\implies\boxed{w=\frac{b+e}{a+b}}$$