Can someone explain how this formula is working? I believe it is being used to return the smallest value in column E.

=LOOKUP(2,1/(E:E<>""),E:E)

Seems to me that it returns the contents of the last cell in the column that is not blank.

The 3 arguments of the function are the lookup value, the lookup vector, and the result vector. So basically we're transforming column E, looking for the value 2 in that transformed vector, and returning the actual value in column E that corresponds to the position we found 2 in the transformed vector. The transformation is basically replacing all non-blank cells with the value 1, and all blank cells with an error. Then, when it looks in that transformed vector for the value 2, it doesn't find it, and instead returns the last position that has a 1 (ie the last non-blank cell).

As far as how the transformation works, E:E<>"" creates a TRUE/FALSE vector for whether each cell is non-blank. 1/ that vector converts the TRUE's into 1's, and the FALSE's into errors. If you'd used * instead of /, you'd get 0's for the FALSE's, and the formula would always return 0.

ETA: After typing all that out, I just googled my description in the first sentence and found this -

https://exceljet.net/formula/get-value-of-last-non-empty-cell.