It's an unreasonable fight - the fighter hits twice as hard as a level-appropriate monster, but has half the hit points. The fight is basically rocket tag.
The Veteran is a monster similar to a 5th level fighter.
An 14 con L 5 fighter with the Tough feat has 10+6*4+4*5=54 HP. The Veteran has 58 HP.
The L 5 fighter with 16 strength has a +6 to hit and attacks for 1d8+5 damage per swing one handed (Dueling) x2. If they have 2 shortswords they instead attack for 1d6+3 times 3.
This
nearly exactly matches the Veteran. The LS Veteran version does 2d10+6 (17) vs the Fighter LS 2d8+10 (19). The SS Veteran does 3d6+9 (19.5), same as Fighter.
The L 5 fighter has second wind (1d10+5) and an action surge on top of the Veteran and 1 additional point of proficiency.
So, literally, if you dropped a L 5 fighter into a game you could get a fight that was nearly indistinguishable on the PC side from using a stock Monster Manual Veteran. You could also build the Fighter to be less meaty and more aggressive.
I mean, action surge ain't nothing. The Veteran is probably closer to a L 4.5 fighter.
HP including Second Wind: 44 + 5.5 + 4 = 54
Cut Action Surge for +1 attack/round (a bit of an upgrade; over a 3 round fight, it is 6 attacks instead of 4).
Lose a point of proficiency.
Lose saving throw proficiency.