Splitting multi-line cells into rows and moving the values into another column

Hello everyone.

Thanks for all your help that I've been silently using so far, but I'm driving myself mad with this one and I can't quite make anyone's similar solutions work for me.

I'm supplied with a complex spreadsheet, in which column E often has cells with multiple lines, split with soft returns (alt+enter).

What I need to be able to do, is to split those entries and place each one in a new row, directly below the original, but putting the values in Column B.
I also need to put a value from column B of the original row into column A of each of the new rows.

So, before would look like this:
B4.png
and after like this:
AfT.png

any help would be greatly appreciated and any explanations even greater, thanks.

Thanks OllieB, that was spot on.