This study investigates a desalination system based on a humidification-dehumidification process driven by solar modules and proposes a solution within the framework of equilibrium theory. Although the optimal operation of the considered humidification-dehumidification system has been investigated in the past and despite the simplifications and assumptions characterizing equilibrium theory, the proposed solution provides a thorough understanding of the system operation, which has not been obtained yet. First, it allows an explanation of the asymmetry between the humidifier and the dehumidifier, which results not from mass transport limitations but from the functional dependence of the enthalpy of moist air on temperature, which in turn depends on the functional dependence of the saturation pressure of air. On the one hand, humidifying air becomes easier when the temperature increases, leading to simple wave interactions, to the corresponding smooth transitions, and to greater entropy generation in the humidifier. On the other hand, dehumidifying air becomes more difficult when the temperature decreases, leading to shock interactions, to the corresponding sharp transitions, and to smaller entropy generation in the dehumidifier. Then, it allows description of the behavior of the overall system (i.e., considering the solar modules connecting the dehumidifier and humidifier). Optimal system operation is defined by determining the air-to-water mass flow rate ratio that maximizes the productivity of fresh water for any value of ambient conditions and saline water inlet temperature. Such a maximum productivity curve separates low-productivity and high-productivity regions, with a discontinuity causing a sudden drop in productivity occurring when going from the latter to the former. Such a discontinuity is well explained by equilibrium theory in terms of the operating regimes of the humidifier and dehumidifier. Finally, equilibrium theory is used to derive an analytical approximation of the optimal operating curve. Such an analytical form describes well the actual solution, particularly within the boundary conditions of interest, and provides an immediate tool for easily determining the optimal system operation.