Historians estimate 20,000 Egyptians divided into 4 divisions (Amun, P're, Seth and the newly formed Ptah.) The Hittites most likely had roughly the same numbers.

The battle had three distinct phases.

1) Ramesses feeds his army through the pass one unit at a time. This is a poor tactical decision and could have led to total annialation. The Hittite King Muwatalli, suspecting such foolishness was a trap held back his army in ambush behind Kadesh. Ramesses, perhaps showing a bit of youthful overenthusiasm, led the first division to form twords Kadesh because his scouts had captured and tortured two prisoners who “revealed” the Hittites were at Aleppo (deception, they were plants).
As Ramesses and Amun & Re divisions set up camp southwest of Kadesh they were hit in the flank through light woods that concealed the approach of the Hittite Chariotry (so much for Alexander inventing flank attacks.). At this phase perhaps 1,200 Egyptian Chariots attempted to delay some 2,500 Hittite chariots and failed. Surprise and shock had the Egyptian advance guard shatter. While Ramesses took complete credit for single handedly winning through the Hittite army, in truth historians suspect the Hittites stopped to loot his advance camp allowing survivors to retreat, regroup, and return. (In those days there was no pay for conscripted forces and battlefield/captured city loot was their only reward, other than gold and honor for the bravest).

2) Ramesses led the reformed survivors and joined with the late arriving Ne’arin Chariots (allies/vassels of Egypt) and caught the Hittite forces in dissary, shattering them and chasing many of the Hittite slower chariots into the river. This is probably the brightest moment of the battle for Ramsses, in that he turned a defeat into a victory through sheer will power. Kadesh was open for the taken with a panic stricken routed mob jamming the gates in retreat, when Ramsses men turned to looting the fallen. If you pay men only through loot you must expect success follow up to be haphazard at best.

3) After making another attack the following day, which ended in a draw, Ramsses retreated twords Damascus. While both sides lost heavily, the Hittites held the field. A titular treaty was signed, but whatever increased power Egypt felt it gained was illusional, as shortly thereafter the Hittite control of trade and taxes in the area was manifest. Ramesses, however, sold the entire battle to his subjects as a stunning victory, made possible only by his divine connections.

Jammer

ps; The flank attack was invented on a personal level the day after the shield was invented. Swordsmen constantly try and work to an opponents unshielded side while keeping their shied between them and the opponent. The idea of flanking on larger unit levels was understood from early on, but it took awhile for communications and discipline to catch up to executing it.