The present work deals with the recovery of critical rare-earth elements (REEs) from acidic aqueous solutions. In doing so, we study the adsorption of these ions on ETS-10 titanosilicate. The experimental data are individually fitted with the Langmuir and Freundlich isotherms, and a high adsorption capacity for REEs is found. We further explore the competitive separation of Nd3+ from Ni2+ ions and Dy3+ from Nd3+ ions usually found in aqueous streams generated during the recycling of NiMH batteries and NdFeB permanent magnets, respectively, via adsorption using ETS-10.