The answer is E: an agreement containing mutual promises.
Explanation for each option:
A) An agreement in which a promise is made in exchange for performance describes a unilateral contract, not a bilateral contract. In a unilateral contract, one party makes a promise in exchange for the other party's performance.
B) An agreement wherein at least one party has the right to withdraw without incurring liability does not accurately describe a bilateral contract. This option might refer to a voidable contract, where one party can withdraw under certain conditions.
C) One that appears to be an agreement but lacks an essential requirement for validity describes a void or unenforceable contract, not a bilateral contract. A bilateral contract is valid and enforceable as long as it meets all legal requirements.
D) A judicial remedy to prevent one party from receiving unjust enrichment refers to the legal concept of restitution or a quasi-contract, not a bilateral contract.
E) An agreement containing mutual promises accurately defines a bilateral contract. In a bilateral contract, both parties exchange promises, and each promise serves as consideration for the other.