Solving for the superconducting gap energy integral

I want to solve the integral for the superconducting gap energy in Mathematica as described in this post:

$$\eta\approx\int_{0}^{\delta^{-1}\sinh\eta}\tanh\left(0.882\frac{\delta}{\tau}\sqrt{1+z^2}\right)\frac{dz}{\sqrt{1+z^2}}$$

$\eta$ is a known value depending on the materials, $0\le\delta=\Delta(T)/\Delta_0\le1$ and $0\le\tau=T/T_c\le1$ are dimensionless numbers. I want to find $\delta$ as a function of $\tau$. The author of the original post mentioned that I can fix $\delta$ and solve for $\tau$ for different values of $\delta$, but I don't know the script to make this work in Mathematica. Solve and NSolve do not work for me.

Solve[n ==
Integrate[
Tanh[0.882 d/0.1 Sqrt[1 + z^2]]*1/Sqrt[1 + z^2], {z, 0,
Sinh[n/d}], d]

Any help would be greatly appreciated.