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Find Unique Element in Sorted Array

Write a Python function `find_unique_element(arr)` that takes a sorted array `arr` as input, where every element appears exactly twice except for one element that appears only once. The function should return the element that appears only once.

#### Example Usage
```python [main.nopy]
print(find_unique_element([1, 1, 2, 2, 3]))  # Output: 3
print(find_unique_element([1, 1, 3, 3, 4, 4, 5, 5, 7, 7, 8]))  # Output: 8
print(find_unique_element([1, 2, 2, 3, 3, 4, 4]))  # Output: 1
```

#### Constraints
- The input array is sorted.
- The array contains integers.
- The array has a length of at least 1.
- There is exactly one element that appears only once.
def find_unique_element(arr):
    """
    Find the element that appears only once in a sorted array.

    Args:
    arr (list): A sorted list of integers where every element appears twice except one.

    Returns:
    int: The element that appears only once.
    """
    # Implement the function logic here
    pass
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