Tell me please If it is possible to use "the" before "two" in some situations. For example, I am at a shop and I ask the salesman to show me the best suits he has. So he gets me one suit and then another and I say "I will buy the two."
I will buy two of them.
means you will buy two of the same suit.
I will buy the two of them.
means the same as
I will buy both of them.
so you will buy one each of the two suits you were shown. For clarity you could say
I will buy the two suits you showed me.
The definite article is valid.
Yes, the can come before numbers like in your sentence, but if the subject is not introduced, you will need to include more information:
We have your shoes in two other colours: red and black. Which do you want?
I'll buy the two [pairs of shoes].
As mentioned in the comments, in English there are different phrasings of your sentence that are more common, if that is what you prefer:
I'll buy the two of them.
I'll buy them both.
I'll buy both of them.