B767 Captain reported failure of the #2 engine anti-ice system during climb. Flight returned to departure airport.

Narrative

We were climbing through FL 240 and OAT dropped below +10C while in IMC. When ENG A/I was selected 'ON' we got a R ENG A/I light. Understanding the switch logic... we gave it about 20 seconds then went to the abnormal checklist and requested a lower altitude in search of warmer air. After running the checklist the malfunction remained. I contacted Dispatch via SATCOM and the decision was made to return to ZZZ. After discussion with Dispatch we decided to dump fuel prior to landing. Dispatch 'ran the numbers' and asked us to dump for a landing weight of 370;000lbs. We asked for vectors from ATC for a suitable location for the dump. We were very deliberate and methodical with our planning and management of checklist; communication and flying the aircraft. After all checklist were caught up; we began dumping (See below for details). After completing the dump we requested runway XXR at ZZZ as it was the longest runway with an ILS. Approach and landing were made without incident and landing was smooth with very little impact and no side loading on landing gear. During the approach phase ATC [gave] priority handling. (In my opinion that probably came a result of us requesting a certain non-standard runway). During taxi to the gate... the brakes did get hot (6) but had begun to cool by time we parked. Once maintenance personnel were on board; they had me release the parking brake in order to aid in the cooling of the brakes.Once at the gate we had 3 main. writeups... R ENG A/I; OVERWEIGHT LANDING and HOTBRAKESMy crew (flight deck and cabin) did an outstanding job with every single part of the process. Both the FO and Relief Pilot were spot on and could not have performed better. All things considered it went very well and is a true testament to our training.DUMP INFO Began FOB 119;200lbs Ended FOB 93;300lbs Amount dumped 25;900lbs