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In this work, we study a model of holographic dark energy using FLRW cosmology in the context of modified gravity. An extension of the symmetric teleparallel gravity is obtained by considering the gravitational action $L$ is given by an arbitrary function $f$ of the non-metricity $Q$, where the nonmetricity Q is responsible for the gravitational interaction, and of the trace of the matter-energy-momentum tensor $T$,so that $L=f(Q,T)$. We govern the features of the derived cosmological model in view of the relation between cosmic time and redshift as $t(z)=\frac{kt_{0}}{b}f(z)$ where $f(z)=W\left [ \frac{b}{k}e^{\frac{b-ln(1+z)}{k}} \right ]$ and $W$ denotes the Lambert function, and discuss the evolution trajectories of the equation of state parameter and stability parameters in the evolving universe.
