Given the head pointers of two linked lists, add them and return the new linked list. Each linked list represents an integer number (each node is a digit).

Here is a Python solution for the problem:

class Node:
    def __init__(self, data=None):
        self.data = data
        self.next = None

def addTwoLists(first, second):
    prev = temp = None
    carry = 0
    while(first is not None or second is not None):
        fdata = 0 if first is None else first.data
        sdata = 0 if second is None else second.data
        Sum = carry + fdata + sdata

        carry = 1 if Sum >= 10 else 0

        Sum = Sum if Sum < 10 else Sum % 10

        temp = Node(Sum)

        if head is None:
            head = temp
        else :
            prev.next = temp 

        prev = temp

        if first is not None:
            first = first.next
        if second is not None:
            second = second.next

    if carry > 0:
        temp.next = Node(carry)

    return head

This Python function addTwoLists takes two linked lists first and second as input. It creates a new linked list where each node is the sum of the corresponding nodes in the input lists. If the sum is greater than 10, it carries the value to the next node.

The Node class is a simple linked list node class with a data field for storing the node's value and a next field for pointing to the next node in the list.

The addTwoLists function iterates over the two input lists simultaneously. For each pair of nodes, it adds their values together (along with any carry value from the previous node), then creates a new node with the sum. If the sum is 10 or more, it sets the carry value to 1 and reduces the sum by 10. The new node is then added to the output list.

If there is a carry value left over after all nodes have been processed, a final node is added to the output list with this carry value.

Finally, the function returns the head of the new linked list.