Using Solve[] to find Eigenstates of a 1D Double Dirac Potential


I’d like to Solve

$ $ k^2 \equiv – \frac{2mE}{\hbar^2} = (- \frac{mA}{\hbar^2} (1+ e^{-2ka}))^2 $ $

for E, in terms of m, $ \hbar$ , A, a.

I tried using the following command:

Solve[-((2 m ene)/h^2) == (m^2 A^2)/h^4 (1 + E^(-2 a*Sqrt[-((2 m ene)/h^2)])), ene] 

Isn’t working well for this task. What do you recommend? At first glance it seems it could not be simple to solve "by hand".

Background: This problem comes from Solving a 1D Quantum well with 2 Symmetric Dirac’ Deltas $ \delta_a$ and $ \delta_{-a}$ , where $ A$ is the amplitude.