I've just up-voted CowperKettle's answer, but on second thoughts, I agree with only the first part.
The is the definite article. When you use it, you think that your listener/reader already knows the thing being referred to, or that he will be able to understand what you are referring to from the context.
I agree with this part. I am just another English learner, but I want to know if what I feel is correct.
I think that either 'two of us' or 'the two of us' might include the speaker, but not necessarily.
Also, I think when there are only the speaker and his son in the living room, the father starts to talk about his idea by saying "Two of us are going to the market." Here it doesn't matter how many are in the family. It's the same 'two of us' as spoken by any couple of people meaning 'you and me.' And this is the reason it implies 'excluding the rest.'
And when he talks more about the idea, I think it's natural to keep saying 'two of us' or 'we.' (This is when talking among the two person.)
When 'the two of us' includes the speaker, it might be just an alternative expression to talk about the two already mentioned, but I think it gets to sound like the speaker is being objective or a story teller, or shifting his point of view to the third person. (You use 'The two of us' to talk about us to someone else.)
I would like a confirmation or correction from native speakers.
I have another situation: I think it's natural to start speaking by saying "Two of them look sad" while watching the two people sitting in some distance, though "The two of them look sad" is also natural without any context because you are watching them. Am I correct?