<p>To address the challenges in engineering, social sciences, and large-scale limitations of traditional methods, this paper modifies a nonnegative conjugate coefficient to construct a search direction. This search direction has the sufficient descent property and trust-region feature without relying on any line search approaches. By combining this with line search approaches and projection techniques, this paper proposes a modified two-term conjugate gradient-based algorithm, specifically for solving constrained nonlinear equations. The global convergence of the proposed algorithm is established without the need to require the Lipschitz continuity condition of nonlinear equations. Numerical experiments demonstrate that, compared to similar algorithms, the proposed algorithm is efficient and competitive in terms of the number of iterations, the number of function evaluations, and the running time. Additionally, it has been successfully applied to deal with image denoising problems.</p>