Catalyzes the electroneutral exchange or flux of physiologically important metabolites such as dicarboxylates (malonate, malate, succinate), inorganic sulfur-containing anions, and phosphate, across the mitochondrial inner membrane (PubMed:29211846, PubMed:38780415, PubMed:38937634). Substrate exchange across the membrane occurs consecutively with one substrate being transported first, then dissociating from the substrate binding site before the second substrate binds for transport in the opposite direction (PubMed:38937634). Does not transport glutathione (By similarity). Plays an important role in gluconeogenesis, fatty acid metabolism, urea synthesis, and sulfur metabolism, particularly in liver, by supplying the substrates for the different metabolic processes. Regulates fatty acid release from adipocytes, and contributes to systemic insulin sensitivity (By similarity). {ECO:0000250|UniProtKB:Q06143, ECO:0000250|UniProtKB:Q9QZD8, ECO:0000269|PubMed:29211846, ECO:0000269|PubMed:38780415, ECO:0000269|PubMed:38937634}. This is the function of SLC25A10 (solute carrier family 25 member 10, Ensembl gene identifier ENSG00000183048).