Not a solution, but when you bring the first equation into normal form you find that it is a 3rd-order polynomial in "i" divided by some simpler stuff. Trying to find the root for this numerator (the 3rd-order polynomial), my version of Maple (15) has a hard time... and by inspection it is clear that the situation wrt. "c" is no better. I have not used Maple's facility for solving such polynomials; in principle, 3rd-order polynomials do have solutions. A possible way out may be to replace all the coefficients of the powers of "i" with simple variables; solve that system & back-substitute. Do the same with "c" and see if you can get rid of the cross terms (the "i" in the solution for "c" and vice versa). BTW, there may be complex solutions.
At any rate, faced with expressions like this Maple usually needs some help and guidance, which is to say that you want to break-down the problem into manageable chunks. In doing so you will find where it has difficulties. The CAS that eliminates the need for our thinking has yet to be developed...
PS: After nearly 10 min CPU I get this:
[Length of output exceeds limit of 1000000]
where subxpr2 is the numerator of the normal form of your first equation.