Can I install a subpanel using only two ungrounded (hot) conductors and a grounding conductor?
Without pulling an additional wire, you'd only be able to install a 240 volt subpanel.  You won't be able to install a proper 120/240V subpanel with only two ungrounded conductors and a grounding conductor.  If you want 120 volts, you'll have to pull a proper grounded (neutral) conductor.