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 nonmetricity Q, where the nonmetricity Q is responsible for the gravitational interaction, and the trace of the matter energy momentum tensor T, so that L=f(Q,T). We expand on the features of the derived cosmological model in view of the relation between cosmic time and redshift as t(z)=kt0/b*f(z) where f(z) = W[b/k*e((b-ln(1+z))/k)] and W denotes the Lambert function, and discuss the evolution of the trajectories of the equation of state parameters and deceleration parameter in the evolving universe using a special then generalized version of the model.