NTs don't "lack" the ability to apply emotions to our judgments. Rather, we generally refuse to. As for expressing emotions, it really depends on what you're talking about. NTs generally aren't "emotive", but if you never observe any emotions being expressed by an NT, you're just not watching. "T" just means that when you, the REAL you, decides to do something, it will generally be based on objective criteria/standards/reasoning, and not subjective (e.g., emotional) criteria/standards/reasoning. T doesn't mean one is smarter, or better at thinking or imply any degree of skill - it's just a personal preference.
W/r to writing emotions, I think that may be more of an INxx thing, and to a degree an Fi thing. It's an Fi thing, partly, because Fi takes a while to ponder before being able to express emotions with any degree of precision. Usually, those who prefer Fi tend to become more quiet the more strongly they feel emotion. Writing, taking the time to write, gets around the inhibition in a couple of ways: 1) there's no one in your face, 2) you get some time to think about how you feel before you write it down.
Personally, I find that my emotions, when I want to express them, are usually a big massive ball of incoherency when I look at them initially. If I'm lucky, I know whether they're positive or negative, but usually, they're just there. I let myself relax and ponder them for a while, and then they become more clear. Once I understand them well enough, I can communicate them, but I don't feel comfortable with most methods other than writing. Speech is just too brief, and it doesn't feel like what I'm saying is "really true", but only a vague approximation of what I feel. If I have the luxury of time, I can create something that describes how I feel, as long as the emotions aren't too intense. (Intensity implies that I've not processed them much, if at all, yet.) That creation is usually prose, but occasionally might be music or some other work of art.
In spite of my ability to do so, it isn't easy. I am very much more comfortable talking about ideas than emotions, and oftentimes I will express emotions more abstractly and impersonally in order to describe what is going on, rather than make direct statements about what I feel.