First, fsolve does not solve bound constrained problems. (What you have.)
Second, even if it did, fsolve does not solve problems with discontinuities in it, or singularities of any form. You have absolute values in there. You have calls to the function sign.
Third, fsolve does not solve problems with symbolic unknowns.
Need I say more?
At best, you can use a tool like GA, which is capable of overcoming all of those problems. You can formulate the objective function for GA as the sum of squares of all of the residuals to those equations. Note that GA is also not able to solve symbolic problems, so you will need to learn to write this in the form of a function.