Sollen expresses moral duty or the suggestion that something ought to be done. Müssen can express the necessity of doing something, but also the moral duty. Both verbs can express a duty imposed by someone else. In this case müssen is stronger than sollen, implying that the imposing person has some kind of power to make the other really do it.
or, intransitiveshould do (something expressed or implied); to be asked to do (something); to be obligated to do (something); ought to do (something expressed or implied)Was sollen wir tun? — “What shall we do?”Soll ich? — “Shall' I?”Du hättest nicht gesollt'. — “You shouldn't have.”