I just framed something like that, though I only had a 8" difference. Frame it like an upside down bulkhead. 2x bottom plate on floor, 2x studs on flat, 2x2 top plate, nailed into little 18" pieces attaching to a 2x ledger nailed to wall. You following me camera guy? Drywall it. Though 18" might good a good place to get in some woodworking or a countertop. Definitely get sparky in there to run your wires for receptacles and new tv!