I think that part of the story's beauty is that it really does not offer a resolution. In a commitment to present consciousness as it is, Hemingway does not capitulate to traditional storytelling narrative where a resolution is present. In doing so, the realistic manner in which the conversation is constructed would disappear. Instead, Hemingway offers a portrait of reality, complete with the realistic element where an ending resolution is not entirely evident. Part of the reason for this is that the story is constructed and simultaneously concealed by dialogue. The third person narration is present, but it is secondary to the dialogue between the man and woman that allows the full force of the story to be understood. We only know of the discussion's topic through dialogue. It is only through dialogue that we understand more of the characterizations of each character. Yet, it is because of this that there is not a full resolution present nor is there a complete grasp of the force of the situation. In the end, it is this element that prevents full resolution to be recognized.
In Hills like White Elephants, the solution appears in a such a way that the characters leave each other in their hard relationship. They can not solve their problems through conservation. They are both drinking because they are trying to avoid each other.