Series expansion or transform of a modulus expression

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I am solving a set of non-linear equations whose final expression is like:

F=(abs(Equation))^2-k; (Where k is a constant.)

Since, modulus of the equation is involved the solver is unable to resolve the variable associated with phase component. I think if I can express the part: "abs(Equation)" in some series or use some transform technique to avoid modulus in the expression, I can solve my equation. I hope I have made myself clear. Is there any solution to overcome this?

Thanks