Edward was born in Savannah, Georgia in 1738. Nothing is known of his ancestors since he was a foundling. He was raised in the Bethesda Orphan House at Savannah, and educated in the school there. He later taught in that same school. Since he was born only five years after James Oglethorpe shipped the first colonists to Georgia, it is likely that his parents were included with those recruited from debtors' prisons or poorhouses.
Langworthy began working with Georgia's Committee of Safety, and was their secretary when they became a revolutionary Council of Safety on December 11, 1775. The Georgia assembly sent him to the Continental Congress in 1777, and he arrived just in time to sign the Articles of Confederation. He served in the Congress until 1779.
Edward moved to Baltimore, Maryland in 1785. He married a young lady named Wright, and the couple had four children. He also bought a part interest in a newspaper The Maryland Journal & Baltimore Advertiser and became its editor. In 1787 he sold his interest, and became an instructor at the Baltimore Academy.
In 1795 Langworthy was made the clerk of customs for Baltimore, a post he held until his death. He died of Yellow fever on November 2, 1802 and was buried at the Old Episcopal Church. The church was torn down in 1891, and details of any re-interment are unknown.