[Tomedb]

I was told by my Chemistry teacher that E = KE + PE.

When an electron moves up an energy level, I assume it gains potential energy due to a greater distance from the nucleus and loses kinetic energy as it's velocity decreases from a weaker electrostatic attraction.

If that is so, how can an electron gain energy, if the gain in potential energy is offset by the loss in kinetic energy.

[mjc123]

The gain and the loss are not equal. As an analogy, consider e.g. a satellite orbiting the earth. If the zero of PE is taken at infinite distance, then PE = -2KE, so if the satellite moves to a higher orbit it gains twice as much PE as it loses KE. Electrons in an atom are more complicated, but the same principle applies.