I assume that most of the time is spent in the line R = K\E (as this has cubic complexity in the size of A, while the other operations have square complexity). So any changes to the previous lines will not have much influence. You could use the MATLAB Profiler to verify this.
I'm afraid there's not much to be done about the speed of backslash for a general dense matrix of this size, unless the matrix K has some special structure, or if you are reusing the same matrix K multiple times.
Is E a vector, or a matrix with many columns? How is R used after computing it?