I've managed to do this several times in my life, and it's true. Life becomes a lot easier when you simply forgive, absent of any apology.
It's like lifting an enormous weight off your shoulders.
I've also failed to find this type of unsolicited forgiveness at least twice in my life. In both cases, I know that my peace of mind would be far greater if I could just find forgiveness in my heart, but alas, it has thus far eluded me.
Some things are just harder to forgive than others.