what 'splitting the difference' means

How the Book Got Its Title

“If Alberto were still alive, I wouldn’t be here.

Yet my happiness is happening without him.

I can’t stop the grief or the joy, so I’m splitting the difference between them. And soaking up the moment, like he would do with a bit of bread and the sauce left over from a really good meal.“

Thanks to your messages and notes, I’m recommending this excerpt goes on the back cover, above the book summary. Because context matters.