Cohn filed for divorce while Vargas was in a Tennessee rehab
Credit: Jim Spellman/WireImage

When Elizabeth Vargas came home from a Tennessee rehab in 2014, she had no idea her husband would leave her just days later.

“It was brutally difficult,” Vargas, 54, tells PEOPLE exclusively in this week’s issue. “I think anyone can imagine what that felt like.”

Vargas reveals even more in her new memoir Between Breaths (out Tuesday). After battling an alcohol addiction, Vargas was back in rehab after relapsing a third time. While the 20/20 anchor was away, her husband of 12 years, singer-songwriter Marc Cohn, hired a divorce lawyer and started the process – without telling her.

When she checked out of rehab, Cohn was still on tour so Vargas had yet to see her husband when she went on the air for an interview with George Stephanopoulos to tell the world about her addiction.

WATCH: Elizabeth Vargas on Her Struggle with Alcoholism and How She Hit Rock Bottom

“I look at that interview and I look stunned,” she says. “I feel for that version of me because I know looking at myself that you’re about to go home and find out your husband wants a divorce.”

For more on Elizabeth Vargas and an excerpt from her memoir, pick up the latest issue of PEOPLE, on newsstands Friday

Now, in recovery, Vargas says her relationship with Cohen is about co-parenting their sons Sam, 10, and Zach, 13.

“We both love our children and we will be in each other’s lives for the rest of our lives because of these two amazing boys,” she says. “I think we both focus on that.”