I got confused because you defined your functions kappa like variables (which works because you use the symbolics) and so guessed wrong as of the equations you want to solve.
Fortunately Richard was around and guesewd right.
You can also use the derivatives in the solve statement:
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A numeric solve block should work, too. But here you would have to define your functions correctly as functions (kappa(ex,ey,phi):=....) and provide values for all constants as well.
