Why the average yearly temperature at the north pole is -18c while the average yearly temperature at the equator is 27c?

This is due to the tilt in the earth's axis, along with the pole's being a bit further from the sun. The shallow angle of the sun on the north pole means a lot of the heat energy is refracted away from the surface, and hardly any radial heat occurs. However, at the equator, the suns rays are much more direct, and the extremely steep sun angle allows radial heating to occur at high levels.