A system for recovering rare earth elements from coal ash includes a leaching reactor, an ash dryer downstream of the leaching reactor, and a roaster downstream of the ash dryer that is cooperatively connected to both the leaching reactor and the ash dryer. Coal ash is mixed with an acid stream such that rare earth elements present in the coal ash are dissolved in the acid stream, thereby creating (i) a leachate containing the rare earth elements and (ii) leached ash. The leachate is heated to obtain acid vapor and an acid-soluble rare earth concentrate. Mixing of the coal ash with the acid stream can occur in a leaching reactor and heating of the leachate can occur in a roaster. The acid-soluble rare earth concentrate can be fed to a hydrometallurgical process to separate and purify the rare earth elements.