How can I generate and solve a system of nonlinear equations using fsolve?

Hi, I attached the system of equations I'm trying to solve as an image, where y(t), I(t), and 'datos' are given for all t=1960:2010 (the index is not important at all).

I want it to solve for all k(t) with t=1960:2010 and delta by using fsolve, but I don't want to write all of the difference equations and sums, as they may change anytime if more data is available.

In my last attempt, I attempted to create a Matlab function to represent my system of equations in a vector in order to use fsolve, but failed to do it. I could attach the function file if someone requests it, but I don't think it is nowhere near the solution.