Operator manuals from Monarch and other sources are available online, a web search should bring up a current site with one as they have varied over the years. Many of us have them on our hard drives and printed out but they can't be sent over this forum, the files are too large. For beginners the Stanford University one was particularly good. The 10 EE is not a simple machine, mechanical interlocks prevent some ham fisted moves but far from all of them.
The manual for your machine can be purchased (very highly recommended) from this source that is the go to for the parts and information you are going to need while getting your machine up to snuff. 10 EE were all custom built lathes and it's amazing they have the records for your machine and in the collective our machines.
Monarch Lathes | Welcome | Cnc & Manual Lathes Specialists
Your WiaD drive will run off single phase perfectly if it is good. Follow the advice above to determine what voltage it is set up for now. Some machines were dual voltage enabled, some were not. Since the coolant pump is dual voltage check its connections: what voltage is it wired for? That's another clue. It being dual voltage strongly suggests the input transformer is dual voltage also. Inspect as directed above in a prior generous response.
You have a 3 HP spindle motor WiaD (Works in a Drawer) machine. Let's not get into KVA yet, you have a lot to sort out before discussing electrical requirements.
You will receive wiring diagrams in the package you order from Monarch. They will also know if the machine was originally a dual voltage machine. That's another hint but who knows what has happened in the last 60 years? You will after you get to know what you have by examination with knowledge of what to look for.
Another vote here for familiarizing yourself with what is already on this forum free for the looking and searching. You'll never find a deeper source of information about the 10 EE than you can by looking back in this forum. Many of the most knowledgeable are no longer with us for various reasons so this is the only place to learn what they provided.
The coolant pump is three phase, your WiaD drive is not. Hope your machine wasn't trashed by coolant, that is a common scenario with found 10 EE and a big hole to climb out of.