To the best of my knowledge the majority of people that wear Rabeinu Tam Tefilin put it on without a Bracha at some later point in Tefila or after Tefila. Based on this I was wondering is there any source that discusses what Rabeinu Tam did? Did he wear Rabeinu Tam Tefilin exclusively? Did he also wear Rashi Tefilin? What order did he wear them in and on which did Rabeinu Tam make a Bracha?