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 == 
   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.

η = 1;
int[δ_?NumberQ, τ_?NumericQ] := NIntegrate[Tanh[882/1000*δ/τ*Sqrt[1 + z^2]]/Sqrt[1 + z^2], {z, 0, Sinh[η]/δ}]
ContourPlot[η - int[δ, τ] == 0, {τ, 0.001, 1}, {δ, 0.001, 1}, FrameLabel -> Automatic]

enter image description here


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