The moon is brighter than the sun when you measure it in gamma rays. Sorta.
NASA published this interesting factoid in a press release last week while sponsoring research by physicists Mario Nicola Mazziotta and Francesco Loparco of the National Institute of Nuclear Physics in Italy, who conducted observations with the Fermi Gamma-Ray Space Telescope.  Electromagnetic radiation, as we call it, spreads like a wave. Waves have a characteristic wavelength (the distance between their peaks) and amplitude (the intensity). The energy of light is proportional to its wavelength, with shorter wavelengths meaning a higher energy. Our eyes only perceive a small part of the possible light, which we call visible light. For our eyes, the moon looks like a white circle because it reflects visible light from the much brighter sun.
But the moon literally has more to offer than the eye suggests. High-energy particles, generated in the entire universe from exploding stars or black holes in the center of galaxies, fill the room. Although they are usually blocked by magnetic fields, the moon has no magnetic fields. The particles hit the lunar surface, interact with their matter and thereby generate gamma rays. These gamma rays are visible through special detectors such as the Fermi telescope. Because cosmic rays strike the moon from all directions, the gamma moon does not show any phases like the crescents we see in visible light. According to NASA publication, the brightness varies due to cyclic changes in the sun's magnetic field.
NASA points out that the moon only outshines the sun in gamma rays at lower energies, with the sun's magnetic field blocking the cosmic rays. More energetic particles still penetrate the Sun's magnetic field, interact with the Sun's atoms, and produce gamma rays. NASA also mentions that it is important to understand the gamma-ray environment of the Moon as we renew our efforts to return astronauts to the Moon.
The following picture shows the Fermi view of the Moon, which brightens as it gathers more gamma rays.
So, next time you're in kindergarten and Your Teacher Tells If the moon does not light up by itself, you can tell your teacher that this is indeed the case.