lambert w - Solving an exponential function

I have the below exponential function which I wish to solve it for $b$. Other than resorting to the Lambert W function, is there alternative way of representing the solution?

$$\frac{(1+a)(1-b)}{ab +a -b +1} = \exp \left({\frac{2a(ab-a-b)}{ab +a -b +1}}\right)$$ where $a,b \in (0,1)$.

Thanks a lot.