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Let $\Omega\subseteq \mathbb{R}^N$ be a bounded domain. In this article, we investigate the existence of entropy solutions to the nonlinear elliptic problem $$\displaylines{ -\hbox{div}\Big(\frac{|\nabla u|^{(p-2)} \nabla u+c(x)u^\gamma}{(1+|u|)^{\theta(p-1)}}\big) +\frac{b(x)|\nabla u|^\lambda}{(1+|u|)^{\theta(p-1)}}=\mu,\quad x\in\Omega, \cr u(x)=0,\quad x\in \partial\Omega, }$$ where $\mu$ is a diffuse measure with bounded variation on $\Omega$, $0\leq\theta<1$ is a positive constants, 1&lt;p&lt;N, $0&lt;\gamma\leq p-1$, $0&lt;\lambda\leq p-1$, c(x) and b(x) belong to appropriate Lorentz spaces.