Final answer:
The religious movement founded by John and Charles Wesley in the 18th century is Methodism. They were inspired by the writings of Martin Luther and experienced a deep religious conversion, leading them to preach about a personal relationship with God.
Step-by-step explanation:
The religious movement that was founded in the 18th century by brothers John and Charles Wesley is called Methodism. The Wesley brothers, who practiced what they preached, believed in public service and missionary work.
They encountered Moravians in England and were inspired by the writings of Martin Luther, particularly his Justification by Faith. In 1738, both brothers experienced a profound religious conversion which led them to preach about a personal, emotional relationship with God. This preaching would eventually carry over to the colonies.