Complex sentence: By nightfall on 22 March an infantry battalion had crossed the Jordan River and established a bridgehead on the eastern bank and by noon the following day two battalions of the London Regiment were across and attempting to enlarge the bridgehead.
Split into simpler sentences: By nightfall on 22 March an infantry battalion had crossed the Jordan River and established a bridgehead on the eastern bank. By noon the following day two battalions of the London Regiment were across and attempting to enlarge the bridgehead.