Crossword Genius

Junk energy emitted by toothless prime minister (4)

Ross

I believe the answer is:

eden

I'm a little stuck... Click here to teach me more about this clue!

'prime minister' is the definition.
(Anthony Eden, UK PM 1955-57)

'junk energy emitted by toothless' is the wordplay.
I cannot really see how this works, but
'energy' could be 'e' (physics symbol as in E=mc2) and 'e' is located in the answer.
The remaining letters 'den' is a valid word which might be clued in a way I don't see.
This explanation may well be incorrect...

Can you help me to learn more?

(Other definitions for eden that I've seen before include "Paradise - ex-prime minister" , "Leading 11 [CONSERVATIVE]" , "Badly need the garden" , "In need of a great garden" , "Adam and Eve's garden" .)

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