The horror collision happened on Monday, April 2 at about 2.30am at the top of the westbound exit slip road at junction 26 of the M62.
They were travelling in a white Skoda Octavia which collided with a black Vauxhall Insignia, a spokesperson for West Yorkshire Police said.
The spokesperson added: "The black vehicle was travelling the wrong way down the motorway slip road.
"Both men died as a result of their injuries."
A 22-year-old man was arrested at the scene for causing death by dangerous driving, but was released earlier this month pending further investigation.
The force's Major Collision Enquiry team, leading the investigation, have today (Thursday) renewed their appeal for anyone with information to get in touch.
Also in news: Flipped car leads to driver being caught with no insurance for SECOND time this yearThey are urging people who were in the area of junction 26 on or around the time of the collision, who may have seen either of the vehicles prior to the collision and in particular, anyone who has any dash cam footage, to come forward.
Also in news: Quick-thinking girl, 7, helps family escape blaze in Leeds homeOfficers also want to speak to drivers of any heavy goods vehicles who may have been travelling on the stretch of the M62, or any motorists near the Chain Bar roundabout, before the slip road.
Anyone with any information is asked to contact police on 101, quoting log number 212 of April 2.
Information can also be given to independent charity Crimestoppers anonymously on 0800 555 111.