How does a Constitutional monarchy work with both a King and Emperor? ( no separate )?

It can't have both. It has a king OR it has an emperor.

A constitutional monarchy is essentially a system whereby the monarch rules, in theory or in practice, but there are constitutional limitations on their powers (i.e. there are certain things the monarch can or cannot do).

Beyond that, though, it can take basically any form you want, including how many titles the monarch has, if there is anyone else, what their titles are, what they mean, and so forth- often these are more ceremonial than anything else, and what they mean is basically whatever the traditions, customs and laws of that country say they mean.

So for instance, Queen Victoria was Queen of the United Kingdom of Great Britain and Ireland, and also Empress of India later in her reign- she assumed that title basically because she ruled India. But it was basically up to Victoria and the UK as to what her titles would be- she could have been "Victoria, Queen of England, Ruling Princess of Scotland and Empress of that little shop down the road from the palace" if they'd wanted.

As to the historical context as to why she happened to have those two titles in that case, what had happened was that India was originally ruled by the East India Company, which was a corporation with its own private army, governmental structure, etc (it wasn't uncommon for corporations to directly rule territories in those days). After the Indian rebellion, though, the British crown dissolved the company and took direct control of India, so Victoria became its Empress.