Written and first recorded by Jack Lee (1981).
Hit version by Paul Young (US #22/UK #4/GERM #1/IRE #3/BEL #1 1983).
From the wiki: “‘Come Back and Stay’ was written and first recorded in 1981 by Jack Lee (‘Hanging on the Telephone‘), who had earlier formed the seminal, yet short-lived Los Angeles power pop trio The Nerves. In 1983, singer Paul Young released his cover as a single from his album, No Parlez, and it became an international hit; his first US Top 40, peaking at #22 on the Billboard Hot 100.”
Paul Young, “Come Back and Stay” (1983):