Can we linearize $T^2$ When solving $\dfrac{\partial^2 T}{\partial x^2}+\dfrac{\partial^2 T}{\partial y^2}+aT^2=0$ by finite difference? 

I solved $\dfrac{\partial^2 T}{\partial x^2}+\dfrac{\partial^2 T}{\partial y^2}=0$ in Matlab using a finite difference explicit scheme. But when there is a source term, I come up with a system of nonlinear algebraic equations and I can't solve it anymore. 

Is there a better method for solving nonlinear equations without linearizing them?