Here's the answer:

1. Rb4 Kd3
2. Kb2 Ke3
3. Rj4 Kf3
4. Kc3 Kg3
5. Kd4 Kh3
6. Ke5 Ki3
7. Rj8 Ki4
8. Kf6 Ki5
9. Kg7 Ki6
10. Kh8

If Black tries for the opposition with Kc3 instead of Kd3 then

1. Rb4 Kc3
2. Ri4 Kb3
3. Kb1 Kc3
4. Ka2 and White wins on a smaller board.