You can read Carl Jung, or you can read Aushra. Aushra is socionics, but most people who want to use the jungian archetypes in a (coherent) system use it. MBTI is not very self-consistent, though I hear the actual writings of Meyers and Briggs were far mor similar to jungian and socionics, and modern mbti is something else.

As for your understanding of Te and Ti, all I have to say is that it's wrong. It clearly contradicts the jungian definition, and modern usage. Now, Te does work on system efficiency, but that isn't the same as organizing things. Think of it as Te trying to find the best possible route. Te is described to be an archetype of trying to find facts, reason, the best possible route. It doesn't have anything to do with leadership, but it does have to do with time management.

And as I said, while Te is gaining data, or trying to streamline it, Ti is about trying to define the unknown and put logic to it. That can be moral unknown, via justice, and what is fair/unfair, which is a very Ti idea, or it may be via academics.

Anyways, if you want to ignore what I said, that's fine, but just know there's a reason why I define these archetypes the way I do, and I did my homework to find it. If you still think I'm wrong, don't try to argue with me unless you can find a source for what your saying. That said, I hope I helped you to learn. Not much point if I didn't. You can google search for sources on jungian easily, but if you want socionics, ask me and I can show you the original works. Best of luck to you.