Distributed optimization has a wide variety of applications, such as economic dispatch in power systems, social welfare maximization, optimal power flow, where distributed nodes work cooperatively to achieve a minimized global objective function, where the information exchanges among distributed and networked nodes play an important role. However, such information exchanges often suffer from inevitable energy and bandwidth constraints due mainly to their distributed and networked nature. Event-triggered distributed optimization provides an effective means to address this issue. However, designing an event-triggered distributed optimization algorithm with both fast convergence and resource efficiency is challenging. In this paper, a distributed zero-gradient-sum algorithm with a dynamic event-triggered scheme is presented for distributed discrete-time optimization. The triggering threshold is composed of an exponential decaying term and a positive dynamic auxiliary variable. The linear convergence is established theoretically. Finally, this algorithm is applied to an economic dispatch problem to verify the theoretical findings and to demonstrate the effectiveness and superiority of the proposed algorithm.