Question: Solving for Multiple Variables

I'm dealing with an equation of the form shown below:


Basically, I am trying to solve for E in polar co-ordinates, across a radius of r, in a given range of phi = 2*Pi - so, for a given value of r, there would be several values of E around a circle. I was toying with the idea of using the fsolve command to solve for the range of r first, then create a data matrix, then continue solving for phi, but I have no idea how to bridge the gap between the two. Thanks.

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