The student pilot was conducting a solo cross-country flight and was preparing to return to his home airport. After takeoff, he observed a storm cloud along his intended route of flight and elected to return to the airport to wait for it to pass. Prior to touching down, he observed an airplane on the opposing runway flying directly towards him. He veered to the right to avoid a collision and landed on the remaining runway, however, he stated that he panicked and failed to reduce power and apply sufficient braking. The airplane exited the runway, proceeded down an embankment and impacted an airport perimeter fence before it came to rest, which resulted in substantial damage to the left wing. The pilot reported that there were no mechanical malfunctions or failures reported that would have precluded normal operation.