Jennifer, essentially you are solving a system of equations. Do you have the optimization toolbox? If you do then you can solve this either using fsolve or lsqnonlin
Create a function as follows:
function y = nonlinmodel(x,Temp,Amp,Phi)
y = [Amp - x(1)*Temp.^2 + x(2)*Temp.^3; Phi - x(1)*exp(-x(2)*Temp)];
% Where x(1) = a, and x(2) = b
Now you want to find x(1) and x(2) that minimizes the above system in a least square sense.
Temp = randn(100,1);
Amp = randn(100,1);
Phi = randn(100,1);
% Some random data for demonstration
f = @(x)nonlinmodel(x,Temp,Amp,Phi);
optimal_x = lsqnonlin(f,[0;0]);
% OR
optimal_x = fsolve(f,[0;0]);
