def count_achievable_targets(numbers, start, end):
    """
    Counts the number of targets within the range [start, end] that can be
    achieved by adding x and y, where x and y are two distinct numbers in
    `numbers`.
    """
    count = 0
    for target in range(start, end + 1):
        for number in numbers:
            x = target - number
            if x != number:
                if x in numbers:
                    count += 1
                    break

    return count