Solve without Solver

I have the following 5 parameter model equation:

R = Ro + Kc * (1/1 + exp[-(a + b*lnC + c*C)]

where Ro, Kc, a, b, and c are parameters.

The following data is given:

R = 0.0243,0.0698, 0.1531, 0.2573, 0.3356, 0.3994

corresponding values for C:

C = 24, 11.89, 6.11, 2.92, 1.54, 0.75

Without using Solver can Excel be used to determine the optimum values of the parameters?

I think it has something to do with maximum likelihood, but I don't know what else to do. Is there some iterative proces that must be performed?

Thanks