This is good Athenian, though
To be put a few ways:
Te is exercising knowledge and Ti is gaining an understanding.
Te's motive is distinguished, Ti's motive is selective.
Te is technical, Ti is mathematical.
Te may take one solution at a time, observing the process. Ti may input the question into a predetermined equation thus falling full proof of their original understanding.
Te "just the way it is right now" - seeking solution. Ti "whatever doesn't fit doesn't apply" -seeking clarity
Ti may be seen as less rational, but that's because it is less conventional. Most people are extroverts thus most primary thinkers have Te.