Here, we present experimental data and a theoretical model for the dynamics of detachment of hexadecane drops from a solid substrate (glass plate) in aqueous solutions of anionic surfactant and salt, at various temperatures. The influence of the experimental conditions on the motion of the three-phase contact line is investigated. We found indications that water molecules can propagate by lateral diffusion in a thin layer on the surface of the solid plate. The driving force of the detachment process, viz., the imbalance of the interfacial tensions at the contact line, is engendered by the water penetration, while the line friction force compensates this imbalance and determines the stationary speed. Excellent agreement between theory and experiment is achieved. The present study specifies the parameters that can be used to quantitatively characterize the rate of drop detachment, determines the values of these parameters at various experimental conditions, and indicates tools for control of the investigated spontaneous process.