Reach (the noun) is a game term.
The rules for melee attacks say:
Used in hand-to-hand combat, a melee attack allows you to attack a foe within your reach. A melee attack typically uses a handheld weapon such as a sword, a warhammer, or an axe. A typical monster makes a melee attack when it strikes with its claws, horns, teeth, tentacles, or other body part. A few spells also involve making a melee attack.
Most creatures have a 5-foot reach and can thus attack targets within 5 feet of them when making a melee attack. Certain creatures (typically those larger than Medium) have melee attacks with a greater reach than 5 feet, as noted in their descriptions.
Every creature has a statistic called reach that is the range at which they may make melee attacks on a target.
Reach (the verb) is not a game term.
Eldritch Maul says:
For the duration, each of your melee attacks with a weapon or an unarmed strike can reach [verb] a target up to 15 feet away from you, as inky tendrils launch toward the target.
This does not increase your Reach (the creature statistic). "Reach" here is used as a verb to assign a particular usable range to the Eldritch Maul ability. It does not add anything to the creature statistic Reach.
In contrast, Fangs of the Fire Snake adds 10 feet to your Reach (the creature statistic):
Your reach [noun] with your unarmed strikes increases by 10 feet for that action
This actually increases your reach. If we have a natural reach of 5 feet, and we use Fangs of the Fire Snake, now our reach is 15 feet.
Since Eldritch Maul uses a bonus action, it will always come before Fangs of the Fire Snake, if they are to be in effect at the same time. Let's break this down.
Bonus action Eldritch Maul. We can now reach targets up to 15 feet away with unarmed strikes. Our reach (creature statistic) is still 5 feet.
Attack action, spend a ki point to activate Fangs of the Fire Snake. This adds 10 feet to our reach (creature statistic) when we use unarmed strikes, bringing our reach to 15 feet for unarmed strikes.