Branch moved to Washington City with his uncle when the latter took the position as Secretary of the Navy and he was tutored by Salmon P. Chase.

He pursued a preparatory course under a private teacher in Washington, D.C., before going on to train at North Carolina's Bingham Military Academy.

He also attended the University of North Carolina at Chapel Hill for a short time and, in 1838, graduated first in his class from Princeton College before going to study law in Nashville, Tennessee, where he also owned and edited a newspaper.

In 1840, Branch moved to Tallahassee, Florida and was admitted to the bar to practice law by a special act of the legislature.

Branch arrived on the field around 2:30 PM, in time to help stop the Union advance, thus saving General Robert E. Lee's right flank from a crushing defeat.

Soon after this victory, Branch stood talking with fellow brigadier generals Maxcy Gregg, Dorsey Pender, James J. Archer, along with Hill and General Lee when a Federal sharpshooter, seeing the group, fired a shot that hit him in the right cheek and exited behind his left ear, killing him instantly.

Five other memorial cannons are placed throughout the Antietam Battlefield marking the locations other commanders lost their lives.