By the 'duo' Elaine Paige and Barbara Dickson..."I Know Him So Well" is a duet from the concept album and subsequent musical Chess by Tim Rice, Benny Andersson and Björn Ulvaeus.
https://app.box.com/s/i1grtfd4vkf11hx48nackmh0c1k28n4c
Piano and Flute to keep it simple
KenH