The soldiers were engaged in hand-to-hand combat with the enemy.

战士们与敌人展开了肉搏。

《新英汉大辞典》

Our ships have engaged with the enemy.

我方战舰已同敌人交火。

youdao

Understanding the potential for catastrophe, Staff Sgt. Miller boldly charged the enemy and accurately engaged the entire force with his squad automatic weapon, thus eliminating the threat.

充分了解大难即将临头，在此千钧一发之际，米勒上士挺身而出，勇敢地冲向游击队，以他的班用机枪的全部火力，准确地压制住了游击队的火力。

youdao

When his ammunition was depleted, he engaged the enemy in hand-to-hand combat until he was killed.

WHITEHOUSE: President Obama Awards Medal of Honor to Korean War Heroes

He then reported the situation and engaged the enemy with a hand grenade, providing suppression as another Ranger moved to his position.

WHITEHOUSE: Medal of Honor for Sergeant First Class Leroy Arthur Petry

While crossing the courtyard, Staff Sergeant Petry and another Ranger were engaged and wounded by automatic weapons fire from enemy fighters.

WHITEHOUSE: Medal of Honor for Sergeant First Class Leroy Arthur Petry