The two cars exploded as they passed through two checkpoints close to each other on a road outside the border city of Rafah, the sources said. No group claimed responsibility for the attacks.
The army said later on Friday the attacks had killed and injured a total of 26 soldiers, but did not provide a breakdown of the figure. It said security forces had killed 40 terrorists and destroyed six of their vehicles following the attack.
"Law enforcement forces in northern Sinai succeeded in thwarting a terrorist attack on some checkpoints south of Rafah," the army statement said.
The army posted photos of five dead terrorists in blood-soaked fatigues lying in the sand, though it did not identify which terrorists group it believed the men belonged to.
The insurgents in Sinai pledged allegiance to ISIS in 2014 and adopted the name Sinai Province.
President Abdel Fattah al-Sisi describes Islamist militancy as an existential threat to Egypt, which has increasingly seen attacks move beyond the Sinai Peninsula and deep into the mainland, often targeting Christians.
(Reporting by Ahmed Mohamed Hassan, Yusri Mohamed and Omar Fahmy; Writing by Eric Knecht; Editing by Louise Ireland)