If you are looking for a numerical solution, then this is a rootfinding problem. Use fzero, a tool designed to solve exactly that problem.
xfinal = fzero(@(x) (1+exp(x))./(1+exp(-x)),xstart);
You must supply a value for xstart. Better yet is if you can supply a pair of points that are known to bracket a solution.
Of course, this function has no solution, so it will always fail, but I assume that your true function does have one.
If you have truly tried to confuse things, and your real function is multi-dimensional, then you can use tools from the optimization toolbox. Here one would use fsolve.
If you are looking for a symbolic solution then solve (which requires the symbolic toolbox) is the answer.