Extension
Extension is a coat color gene which affects the presence of black pigment in horses, donkeys, and mules.
Horses make two different types of pigments, red (pheomelanin) and black (eumelanin). The red pigment can make colors ranging from a light yellowish brown to a deep reddish brown, while the black pigment can make colors ranging from a dark chocolate brown to black. Extension decides whether the horse can make black pigment only in the skin or if it can also "extend" into the hair.
There are two alleles to extension*, named e and E**. E is dominant, so a horse with the genotype EE or Ee will have black hairs (and may also have red). A horse with the genotype ee will only have red hairs.
EE or Ee: The horse is bay, black, or seal brown, or based on one of those colors
ee: The horse is chestnut or chestnut based (alternately called sorrel)
*There is also another called ea which is effectively the same as e, except that genetic tests performed before 2000 when it was discovered may have mistaken it for E
**E is sometimes also called "+" or "N"
Donkeys have two known extension alleles, called E and e. At the molecular level these are not quite the same as E and e in horses, however visually they have the same effects.
E can also be called Ed, and e can also be called ed
For more info see https://vgl.ucdavis.edu/test/red-factor-donkey