
Since Seok Hyun is an orthopaedics surgeon, and Jiyeon is a nurse, and they most likely attended 6 years of medical school, so they should be at least 24. They probably worked in the hospital for a few years already (they're quite familiar with the staff and patients), plus hospital work experience, I'm guessing they're around 26-29 years old?
(They could be older, but usually BL manga protagonists don't go over thirty that often.)
It is also worth mentioning that Seok Hyun is still rather "inexperienced" at surgery as he was guided by Jiyeon's uncle.
Additionally, Seok Hyun calls Jiyeon "Hyung", so I'm guessing that Jiyeon is a year or two older than him.
These are just my predictions. We'll never know their actual ages unless the artist publishes a character biography of them.

wow, awesome answer! they do act like they're in their mid-twenties
How old are these two main characters in the present story? >.<