A rigorous, closed form solution for the hydraulic head, sharp interface shape, and position in a confined aquifer bordered on one side by a static interface with intruded sea water and on another side by a constant head boundary is obtained in terms of the Dupuit-Forcheheimer model. Linear and nonlinear differential equations governing the hydraulic head variation with the horizontal coordinate contain a sink term, which is assumed to have a constant strength over the unintruded part of the catchment and linearly decreasing strength through the section overlying the interface. Solutions of the two equations are conjugated. For the length of the freshwater zone a quartic is obtained and solved. An explicit solvability condition is presented. The interface equation includes the commanding freshwater head, seawater level, density contrast between saline and fresh water, aquifer thickness and conductivity, and intensity of smeared losses, which model abstraction from the aquifer.