How to show that the nonlinear operator I+N is onto?

Question

Is it possible to show that the nonlinear operator $I+N:\mathbb{R}^{n}\rightarrow \mathbb{R}^{n}$ is onto, without showing that the nonlinear operator N is contraction? Because we know that if N is a contraction mapping, then it is always true that I+N is onto. But I want without assuming the contraction of N, I+N should be onto.