The function replaces specific lowercase and uppercase letters with other letters as follows: 'e' -> 'b', 'o' -> 'w', 't' -> 'x', 'n' -> 'd', and 'E' -> 'B'.

[CODE]:
```python
def approximate_function(s):
    return s.translate(str.maketrans("eotnE", "bwxdB"))
```
