Thank you Frank, sorry for the late reply, I have been away. I will digest this and try it out. Ta.

I suggest using FindMinimum or NMinimize, minimizing the sum of the squares of the error terms and using your equation as a constraint.

The equation does not have a closed-form solution, given the mixture of linear and exponential terms. It can be solved numerically using FindRoot[equation==0,{I,I_guess}] by putting in values for V and all the parameters. You might also try a ParametricPlot for I(V) for a specified set of parameters.

Another possibility. You could expand the exponentials to give a linear approximation to the equation.