The Pyramid at the End of the World - S10-E8
Trivia: UNIT, and its director Kate Lethbridge-Stewart, was originally going to appear in this episode, but actor scheduling conflicts prevented this - hence the Secretary-General of the UN and the three military officers.
Trivia: The portrait of Queen Victoria visible in the soldiers' camp is not a portrait of the real Queen, but of her as portrayed by Pauline Collins in the Tenth Doctor episode "Tooth and Claw."
Chosen answer: 1) When Stephen Moffat took over he ignored a lot of what had been developed before (there is not in-universe answer). 2) It would have killed Rose, so the Doctor absorbed the energy. His body regenerated before the energy could do a significant amount of damage that would prevent regeneration.