A set of non linear equations can be solved using newton raphson method. But how to solve that set of non linear equations with an inequality constraint?
If there does not exist such a solution, you would have to try to find a value that satisfies the constraint and comes "as close as possible" to satisfying the equation- Prove It's "optimization".
Looking at this problem I suspect you may well have started with a constrained minimisation(maximisation) problem which you differentiated and set the derivatives to zero. If this is the case this is a . You should look at constrained optimisation algorithms.