Final answer:
Brian likely solves the problem of cooking without a fire by heating liquid in a basket to its boiling point, allowing him to cook the eggs without the need for direct flame.
Step-by-step explanation:
In the context provided, Brian tackles the issue of not having a fire to cook eggs by using an alternative method that involves applying heat in a way that does not harm the container.
While it's not explicitly stated how Brian solves this problem, one can infer that he may use a process like the one described where food can be cooked in a basket by making sure the contained liquid reaches its boiling point. This method would allow him to cook without directly exposing the container to the flames, thus preserving it.