The data input for reservoir simulation of low-salinity waterflood in sandstones includes adsorption isotherms, or equilibrium constants for all cation-exchange reactions, and cation-exchange capacity (CEC). We develop a novel method for determination of those functions from the laboratory data of low-salinity coreflooding; the inverse problem is solved; rather, matching is applied. Changing independent time variable to Lagrangian coordinate transforms the governing system for two-phase multicomponent flow into a single-phase system of mass balance equations for each ion and the volumetric balance equation for water. It allows determining the adsorption isotherms for all ions, or equilibrium constants and CEC, from the breakthrough ion concentrations, using the exact solution of ion-exchange inverse problem. Further, the fractional flow and relative permeability can be determined from the effluent water cut and pressure drop histories, using the Welge's and JBN methods; here each data point corresponds to the breakthrough values of ion concentrations. We show that for four-ion waterflooding, only two constants from two equilibrium constants and CEC can be determined. Treatment of five coreflood data sets shows a close agreement between the laboratory data and the results of inverse problem solution.