How is the problem SOLVED in book of city ember?

The problem of Book of Ember is solved when the children, Lina Mayfleet and Doon Harrow, find the original instructions provided by the creators of the city.

The instructions contained within the pipe system of Ember help them decipher and understand the city's mysterious pipe network, its power source, and the way to contact the outside world using a radio set.

Upon discovering the original pipe room with the help of the old, blind scholar named Mrs. Murdo, Lina and Doon successfully restore power to Ember and establish communication with the Surface World. This discovery paves the way for the citizens to eventually abandon the deteriorating city of Ember and migrate to the outside world.