This is a PM I sent to dolphin, but I thought some of it was pretty good, so I decided to post it. It starts off as an explanation of Ti via how LSI supervises SEE, but I went on to explain Te in the second half. The first workplace example it based off of one of Expat's anecdotes, but it's my own spin on it.
Ti is subjective logic, meaning you make judgments based on a concrete, internal set of rules used to verify information and assess the quality of an action or thing.
Here is a hypothetical example:
At work, there is a manager who has been doing things that have caused his subordinates to be upset with him. This culminates in a confrontation between the manager and several employees, one of whom is SEE.
The SEE has formed a negative Fi sentiment toward the manager, and he verbally expresses his feelings by shouting that the manager has failed in his job at the expense of the rest of the employees.
Unfortunately for the SEE, there is another employee present who has sided with the manager and who happens to be LSI. The SEE's remarks toward his superior are perceived as an affront to the LSI's internal system of rules, and he harshly reprimands the SEE, firmly telling him that managers are not to be spoken to in such a manner.
The SEE is helpless to respond, because his method of decision-making is based around his internal sentiments toward whatever is the object of his attention. He doesn't consider the propriety of his actions, and such rules are something that LSIs very astutely accumulate. LSIs have Fi role, which makes them insecure about the ethical ramifications of their actions and words, so they incorporate social etiquette into their Ti perception of reality.
These "Ti rules" that are accumulated by the LSI, though subjective, are often valid and applicable to reality.
Another example is when my SEE friend blurts out embarrassing information in a public setting, like the time they mentioned that one of their friends, who was present at the time, needed braces. I didn't want to bring any more attention to the person in question, so I said nothing. In private, however, I was very strict in telling them what I thought about their comment.
The LSI can be wrong in his supervision of SEEs, but the SEE cannot respond because he knows that he does not consider the "rules" when making decisions. He is a creature of pure impulsive will, not of logic. This is not to say that he can't be highly intelligent, but his goals and decisions will be based off of impulsive desire, not logical analysis.
To clarify the often confusing difference between Te and Ti, I want to go back to the first example and explain how Te would advise the SEE.
Te wouldn't be concerned with the rules being broken. It would instead look at the matter in terms of consequences versus benefits, pros v cons. Very generally speaking, it would probably say something like this:
"I agree that the manager is incompetent. However, a direct confrontation will probably result in the loss of employment, so it's probably not worth it. A better idea would be to anonymously complain to your boss's superiors about his incompetence."
Instead of being smitten by a barrage of Ti rules and regulations, the SEE is given something he can digest: a matter-of-fact statement about the wisdom of his actions, as well as advice on the best alternative course of action.
Here's one more way of looking at it. Say an SEE wants to explore a certain part of the wilderness and needs directions, which either Ti or Te can provide. Te would give the SEE a map with clearly labeled landmarks, warnings, and other useful information that the SEE can incorporate into this impulsive desire to ramble through the wilds.
Ti, on the other hand, would create a detailed, step-by-step series of specific instructions on exactly how to traverse this particular region. The SEE would naturally perceive these directions as boring and overly restrictive, and most likely would end up ignoring them. However, ignoring the Ti instructions causes the SEE, who is without Te backup, to get lost for a week before finally returning home. Upon seeing the SEE, Ti scolds him for not following the instructions, an accusation against which the SEE cannot effectively mount any defense.