I have the following equation: $$\left(\frac{x}{\cosh(x)}\right)^2-x\tanh(x)+\ln\cosh(x)=0$$ and I would like to know if there is some analytic closed form solution.
WA gives me two non-zero solutions $\pm 1.2837768\dots$ which seems intriguingly close to e.g. $ 5/8 \pi\frac{1}{\sinh^2(9877427/9504216)}$. I am wondering maybe there is some closed form solution.
I appreciate any help.