The electrostatic interaction between colloidal particles trapped at the interface between two immiscible electrolyte solutions is studied in the limit of small inter-particle distances. Within an appropriate model analytic expressions for the electrostatic potential as well as for the surface and line interaction energies are obtained. They demonstrate that the widely used superposition approximation, which is commonly applied to large distances between the colloidal particles, fails qualitatively at small distances, and is quantitatively unreliable even at large distances. Our results contribute to an improved description of the interaction between colloidal particles trapped at fluid interfaces.