The pilot reported that he was landing at night with a quartering tailwind. Shortly after touchdown, about the time that he placed the power control lever into reverse position, the airplane veered right. He successfully brought the airplane back to the runway centerline after applying left rudder control. However, about 1 to 3 seconds later, the airplane veered hard right. The pilot tried to bring the airplane back towards the runway centerline again, but the airplane veered off the right side of the runway and travelled through gravel between the runway and the taxiway. Subsequently, the airplane struck a storm trench and substantially damaged the right wing. The airport’s automated weather observation station reported that, about the time of the accident, the wind was from 240° at 13 knots, gusting to 20 knots. The pilot landed the airplane onto runway 17R. The pilot reported that there were no preaccident mechanical malfunctions or failures with the airplane that would have precluded normal operations.