The subject of "Heavenly Hurt" and "internal difference" continues in the third stanza. So no teacher can teach what this kind of hurt and difference is, mainly because it's impossible to define in any absolute kind of way.
That "Any" in line 9 is equally difficult to lock down in meaning. Perhaps the speaker is indicating that "Any" refers to the idea of any internal difference that may exist. No matter who it belongs to, that "difference" can only be understood by the person who holds it. And even then, the meaning may be difficult to fully understand.
So because that "Heavenly Hurt" and "internal difference" is so darn difficult to pin down, it becomes a sort of "seal Despair."
At this point, the extended metaphor of that "Slant of light" has evolved into this new metaphor of a "seal Despair." In a way then, that difficult-to-describe light has solidified as this figurative "seal" that in line 10 appears to be deeply personal and internalized as "Despair."
But what's the speaker so despairing about? Nobody died, nobody's sick, so why all the despair? We thought she was just checking out a "Winter Afternoon."
As we know, our minds and feelings work in funny ways. One minute we're checking out the scenery, the next we're stressing about our despair. The speaker is no different in that way. That initial "Slant of light" opened up the doors to the speaker's internal conflict over her "difference" and her subsequent "Despair."
An imperial affliction Sent us of the Air—
By the end of the third stanza, we're back in the idea of that "Slant of light" that we see here as an "imperial affliction/ Sent us of the Air." So the speaker has managed to connect all the dots between the winter light, the "Heavenly Hurt" it gives, the "internal difference" the speaker feels, and "Despair."
So everything put together makes for this oppressive "imperial affliction," which is a sort of metaphor for an all-encompassing despair. And where does it come from? The "Air," of course, since that's also where the slant of light comes from.
The word "imperial" has a connotation of being everywhere. So not only has the speaker blended all the dots together, but she's also combined the inside and outside worlds in a way that makes them look like one and the same. In other words, the outside world or "imperial affliction" that comes from the air seems as if it's inside too in her "internal difference."
So again we're seeing how the speaker is using natural image to illuminate the speaker's inside world, making the two worlds look quite similar.
And, when we think about despair, the blending of the outside and inside worlds makes sense to us. When we're feeling down, the world tends to look unpleasant, and when we're feeling good, it looks a whole lot better. So although the speaker's diction and metaphors look mighty poetic, she's still getting at some basic ideas we all encounter.