Methods of recovering rare earth elements, vanadium, cobalt, or lithium from coal are described. The coal is dissolved in a first solvent to dissolve organic material in the coal and create a slurry containing coal ash enriched with rare earth elements, vanadium, cobalt, or lithium. The enriched coal ash is separated from the first solvent. Residual organic material is removed from the coal ash. The rare earth elements, vanadium, cobalt, or lithium can then be recovered from the coal ash. The coal ash is mixed with an acid stream that dissolves the rare earth elements, 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. The acid-soluble rare earth concentrate can be fed to a hydrometallurgical process to separate and purify the rare earth elements.