Nodal analysis for nonlinear elements
Try converting R1 and I1 (which are in a Norton equivalent configuration) to a Thévenin equivalent, that way you will have a voltage supply followed by one linear resistor and one nonlinear resistor (after you calculate the series equivalent resistance of the linear resistors you have).

This should give you just two equations, one from KVL and one from the fact that all elements have the same current going through them. The resulting equation for current/voltage will be a polynomial of degree 2.