what motivates him to escape?

Equality knows that unless he escapes and is able to go to the Home of the Scholars, he won't have the opportunity to tell them of his discovery and work with them in finding new ideas.

From gradesaver;

The narrator escapes because no one else would have the originality necessary to even think of escape. Furthermore, although his transgression of omitting attendance at the City Theatre does not seem particularly heinous, few enough people commit any crimes that his case becomes one of paramount importance, leading eventually to questioning from "the most honored Judges of the City." Even Equality 7-2521, oddly, does not think to lie to the Judges, and he still does not wish to be a lonely outcast, retaining hope that he will be able to rejoin his community after he speaks with the World Council of Scholars. He believes that the men who he had once idolized will be greater and more enlightened than the others, but the reader may rightly remain worried that his stint at the Palace of Corrective Detention will foreshadow his reception at the World Council.