Is it possible to solve the following by simultaneous equations?

The logic is that i have an explicit solution for the integral of the left hand side and if i can get the right hand side to look the same by solving for s,a and b, then i can substitute the values to get an explicit solution for the right hand side, but i cant seem to figure it out. there are two possibilities my teacher said.

it satisfies

2s²/aπ(1+b²/a²)²=σ²/2π(1+τ²∗ω²)

or it satisfies this

as²/π(ω²+a²)²=σ²/2π(1+τ²∗ω²)

But i have redone it and I am not convinced it satisfies either with an elemntary solution that doesnt involve square roots. I was told that it would simplify without square roots.