With the Red Factor test, Red pigment (e) is recessive to black pigment (E).
As the chestnut gene is recessive, the horse in question must carry two copies (e/e) to have the chestnut base colour.
The dominant gene being the (E) allows black pigment on the coat so when a horse tests as (E/E) they do not carry the chestnut gene at all.
That means even if they were to mate with a chestnut stallion (e/e), all offspring would receive a copy of each making them (E/e).
The (E) trumps the (e) and thus the offspring will all be bay to black in base colour.
In other words, any horse that is (E/E) will never be able have chestnut foals regardless of who it mates with!
Here is a link to Equine Genetics Research Centre website as well,which has a slightly more in-depth/technical explanation: https://equinegeneticsresearchcentre.horse/coat-colour-and-pattern-testing-2/red-factor/