Example: NiTe dealing with a theory or theoretical argument that is not agreed with.
Faced with an argument/theory, the first awareness (after understanding the argument/theory) is that it must be wrong. The second awareness is why it's wrong, where it's wrong - but this is vague, at a conceptual level. It's there, but not articulated, and it's difficult to latch onto. This flits in and out of grasp briefly, until you can capture the understanding and hold it stable.
That's Ni. Te's job is to double check Ni's work. Te articulates the concept, and the use of words to do so draws in concepts that are attached to those words, broadening the context against which Ni's produce can be checked. Te makes sure that Ni's objection A) works and B) is itself coherent. Te is also what makes it possible to express the objection to others.
Ni then has a tendency to find objections to the objection, flaws in the counterargument - even when they're the last things that you want to find. In this way, the two are able to reject a range of avenues that aren't leading anywhere useful, and to expand, modify and develop new conceptual matter.
Edited to add: This might be summarised more succinctly as follows: Ni gives you fully developed concepts of a certain idiosyncratic nature, whether you want them or not. Te is what you then do with them - build them into theories/models (with constant new input from Ni), formalise them so that you can tell people about them, act on them, etc.