If the 2010 has the same wheel well dimensions as the 2011, you should be able to get 35x12.5 if your wheels have the same offset-back spacing as the Raptor wheels.
I am running 35x12.5 on 17" Raptor wheels with a 2.5 inch leveling kit with no rubbing even with "tame" off-road driving in the mountains. A check of vertical clearance at all stages of turn suggests for HWY driving there should be no rubbing or if there is any rubbing it would not require more than 1-2 inches of trimming the lower inside plastic molding.
I recommend the Auto-Spring Company 2.5 front - 3" rear leveling kit ($~185, $585 mechanic installed & aligned). The ride is the same as factory, no need to change shocks, electrical or hydrolic lines & no rub with 35x12.5 tires at any stage of turn.