Express non-linear algebraic equation in terms of variable $\nu$

Question

I have the following equation that I would like write explicitly in terms of $\nu$, $$\frac{8\epsilon\gamma^2}{A(8\epsilon\gamma^2)-\nu^2}\left[\lambda-\frac{\beta\nu}{2\gamma}E_1+\frac{\beta\nu^2}{8\epsilon\gamma^2}E_2\right]-\left(\frac{2\beta\epsilon\gamma\nu}{A(8\epsilon\gamma^2)-\nu^2}E_3+\frac{\beta\nu^2}{8\epsilon\gamma^2}E_4\right)^2 = 0,$$ where $\epsilon,\gamma,\lambda,E_1,E_2,E_3$ and $E_4$ are constants. Is there any way one can do this? Advise on close approximations or simplification techniques will also be very much appreciated.