First, let's define an external conflict and resolution, then you can probably identify them in this story yourself. An external conflict (conflict: battle of one sort or another) is one that exists between a character (principally the protagonist) and some idea, action, event, person or circumstance that is not part of him- or herself. Here are some examples. If my kitty is playing ambush with my ankles, that is an external conflict. If my business partner is embezzling money, that is an external conflict. If I am trying to save my family from an onrushing tsunami, that is an external conflict. By way of contrast, if I am trying to get the courage to confess to my business partner that I am embezzling money, that is an internal conflict: to tell or not to tell.
Let's apply this to the story and see what the external conflict is. Tom has an all-important yellow sheet of paper. He sees all his ambitions and hopes tied up in what is written on that sheet of paper:
He thought wonderingly of his fierce ambition and ... of the hours he'd spent by himself, filling the yellow sheet that had brought him out here.
The yellow sheet of paper is external to himself. This yellow paper flies out the open window of an upper story New York apartment building and is blown along the ledge in the cold until it catches on a corner ornament. Tom feels compelled to go out on the ledge, face and chest pressed against the cold brick, to retrieve it (this decision, by the way, comes out of an internal conflict):
And he knew he was going out there in the darkness, after the yellow sheet fifteen feet beyond his reach.
Once he is in the external night air, away from the safety of his apartment, he battles the external cold, ledge, brick wall, danger of a misstep, all the parts of his external conflict that are battling against his quest to retrieve his yellow sheet of paper.
This is Tom's external conflict: Tom is battling nature and battling his physical limitations against a raging nature (as raging as it can get on a quiet winter night in downtown New York). Tom must overcome the conflict of impossible, worsening odds and elements at great heights to (1) get the yellow paper, (2) get safely back to the window and (3) get safely back in through the window to his apartment.
You have but to read the end of the story to see how this conflict is resolved, brought to a conclusion, an ending. The interior of the story details in great minutia the agonizing step-by-step journey Tom takes through the external conflict in the eight minutes it takes to go "fifteen feet" and back again to return to where he started. The external conflict is resolved when Tom succeeds in punching his fist through the closed glass window, removing the glass shards and crawling into the safety of his living room. Tom has triumphed in battling external conflict.
Note that internal conflicts may not be resolved at this point, but the external conflict is resolved. Also note that the warm hall gust of wind and the yellow paper invite Tom to a second external conflict, but Tom wisely ironically and derisively laughs it off and goes to find Clare.