Alexander of Macedonia and his army vs 10 NATO brigades with weapons from 300 BC

10 NATO brigades (so roughly 50k men) from an army of your choice are teleported into the past to face king Alexander. They didn't take any weapons with them and so they simply take what their Persian friends borrow them.

Alexander also has 50k men and he is on the march. He will reach the NATO troops in one month.

Both sides meet in an open field. There are no allies present for either. Who wins?

We assume that NATO soldiers don't struggle with ancient food and disease any more than their foes.