I don't believe there is a closed form solution to the equation , so instead you should use a numerical technique to find a very good approximation for the value of x.
I'm trying to find the minimum of the following function:
My working so far:
Where we set the derivative equal to zero as we're trying to find the min.
However, I'm not sure how to solve this equation, and find an expression for x. Is it best to rewrite the hyperbolic tan in terms of e?