"sort out" is a phrasal verb mainly used in the meaning of "resolve/solve" while "sort" can be anything from "searching through" to "separating according to some features". In your example, the proper one is "I'll sort it out", doesn't mean you won't hear the other one in life.

The verb 'sort' is widely used in British English to mean 'deal with' a situation. It isn't wrong and it isn't lazy. For example, anyone who has been on a train anywhere in the UK, or even just passed through a station, will have seen this sign everywhere and heard this announcement many times: See it. Say it. Sorted. This slogan is part of a public safety campaign encouraging passengers to inform rail staff about anything suspicious which they see. Here, 'sorted' means 'Problem solved'. If it's good enough for the British Transport Police, it's good enough for me.

Thank you Layne!

"You will sort it out" I would say this to somebody who has caused a problem and needs to fix it. They need to "sort out" the problem. It's almost slang "You will sort it" I would say this to somebody who needs to organise(organize) a mess "Organize" used in the U.S.A. "Organise" Used in Australia, Canada, United Kingdom, New Zealand