When you "can tell" something, it means that you know it based on something you saw:
I can tell that you're lying to me.
Could you tell I wanted to leave?
You can leave "that" out in casual conversation, but in formal speaking or in writing you should definitely include it:
I can definitely tell that you're improving.
Use "___ can tell ___" to talk about things that someone noticed out on their own. Don't use if for things that someone heard from other people. In that situation use a phrase like "I heard ___":
I heard you and Desmond weren't getting along.