Romans 12:19-21 — Dearly beloved, avenge not yourselves, but rather give place unto wrath: for it is written, Vengeance is mine; I will repay, saith the Lord.
Therefore if thine enemy hunger, feed him; if he thirst, give him drink: for in so doing thou shalt heap coals of fire on his head.
Be not overcome of evil, but overcome evil with good.
avenge not — tied to verse 18.
The wrath of God in Romans (1:8; 2:5, 8; 3:5; 4:15; 5:9; 9:22). It is God's prerogative, leave it to Him.
Proverbs 20:22 — Say not thou, I will recompense evil; but wait on the LORD, and He shall save thee.
Proverbs 24:29 — Say not, I will do so to him as he hath done to me: I will render to the man according to his work.
Showing kindness to an enemy may lead to his repentance and destroy him as an enemy.
The quote is from Proverbs 25:21-22 — If thine enemy be hungry, give him bread to eat; and if he be thirsty, give him water to drink: for thou shalt heap coals of fire upon his head, and the LORD shall reward thee.