Ti seems like a thinking process that is very specific and exacting. It focuses on the details and likes understanding how things work at the bare minimum. As such, they can build from the bottom up. The goal of Ti is to be logically consistent instead of being productive. Ti tends to serve as the backbone or the moral/ethical foundation of a individual; Nothing doesn't seem right or wrong, it has to be logically proven so. Because it's very specific and exacting, it requires a lot of information and people with high Ti tend to be quite creative and knowledgeable.
The main difference Ti has with Te in my opinion is that Te is more focused on the answer or the result. Ti seems to focus on finding exceptions to the rules while Te focuses on the rules simply because it's the more likely thing to happen but, if that particular exception happens, there's already a plan for it. Ti, on the other hand, seems focused more on the debate and the process of learning by comparison. Te prefers structure and order, and that tends to correlate with thought. Te, by nature of function, tends to be more practical and its attention deals more with what can be manipulated.