Read official English at Manga.Club:
There are hundreds of manga about skillful doctors already, but among them "Doctor Enma" offered a different kind of entertainment. Mitsuya Enma was known as a "Speed of Light Surgeon" that can conduct any operation successfully in a short time. The only person he couldn't save with his hands is his little sister, forcing him to involve with drugs trafficking to collect treatment money. He was arrested and put in a cage, but one day, a mysterious, beautiful woman, Kanon, helped him jailbreak on one condition; to serve as a black-market doctor that has to do a time-limited illegal operation with Kanon as the assistant.

From Mangahelpers:
Enma Mitsuya was a highly skilled and swift surgeon, who was widely called the "Light Speed Surgeon." However, behind his bright and promising career lay a dark secret. His little sister Mitsuki was desperately sick, and he had turned to criminal means (such as selling drugs on the black market) to pay for her continuing medical treatment. He could not keep his cover forever, and all his hopes ended when he was finally arrested and sentenced to 13 years in prison.

A year into his sentence, a strange young woman named Kanon, dressed in a black nurse uniform, comes to visit him. The deal she offers may be his only chance to save his little sister. She has arranged with the prison for him to spend his nights in a jail cell with a tunnel that will allow him to escape. On every night, she has a task for him: he will sneak out and be whisked off to a clandestine surgery in Kanon's "Black Ambulance." For each life the disgraced surgeon saves, he will be paid well. He can only hope that what he makes in his new career as a "Dark Surgeon" will be enough to preserve his sister's life while he finishes out his sentence... [tethysdust]