You did not mention if they are aware of each other. You also did not mention if T lives with you or just spends a lot of time at your apartment. These facts are important in a situation like yours. I say this because your position is complicated enough without the element of deception in the mix. By that I mean that you have a very complicated set of decisions to make and you are very concerned about hurting one of them and if they do not know about each other they could feel decieved and be even more hurt.
You also didn't mention if T thinks you already are a couple and if you are in a committed relationship.
I was in love with two people once and very much like your situation. They both had attributes that I loved and choosing was very difficult.
I can tell you that it tore me in two for many months and caused me to have tension headaches and horrible guilt.
You basically carried on with your life and found someone who gave you what you wanted and needed from a man. Then your ex stepped up and showed you the emotions you had always wanted and became what you had always wanted him to be.
I don't think it is a matter of being able to decide what you want while you are able to have them both. I truly believe you need to separate yourself from both for a while until your heart tells you which one you truly yearn for. I think that J would or should understand that you have been seeing someone else and he should know as soon as possible. The situation with T will be a little harder if he is living with you. Living by yourself and giving yourself the time you need to figure this out is important and T should be able to understand that you need some alone time to decide where your life if going. If and when you decide to see either of them again, they should both know about the other. If you are not open and up front you run the risk of loosing their trust and respect. Honesty and being open about their feelings is what you respect in both of them so I am sure it is important for them to recieve it from you. As long as you can see each of them and have them around you when ever you want, you will not be able to decide which one you cannot live without. You could live with either, but the stronger emotion that will haunt you for the rest of your life is...Which one could you "Not" live without. You will know eventually, even if you have to date them both openly for a while. The one that wants you to be happy will hang in there. The one that loves you the most will go the long haul. The one that loves you the most will not give up.
