Can I upgrade Win7 Ent to Win10?

As long as you do 7 Enterprise > 10 Enterprise, all will be fine! You can use the 7 key to activate 10! :) (Upgrade)

But you can't transfer one key to another pc as it is tied to your PC.

As far as I know, Enterprise does not qualify for the free upgrade. For one thing its (normally) Volume License activated. Its excluded from the offer as its not a consumer version. Any Windows version that is VL activated is excluded. VL keys are tied to the company that bought those licenses, not to the physical hardware they are used on.

It's not a one time license for Enterprise, like it is for other editions. Not normally anyway. Enterprise is Volume Licensed by corporations. I think its a yearly fee, and you can't just buy one license. Its only economically feasible it your buying multiple licences for large corporation. I don't know all the ins and outs of it, but that's my understanding. The only exception is MAK licenses that are meant for testing. I get those as part of my My Visual Studio Subscription. Like I said though, they are for testing in leu of a VL key. You can't buy those separately.
What version of Windows 10 is the laptop running? And is it OEM or Retail? You may be able to transfer that license from the laptop to the desktop? You'll have to stop using Windows 10 on the laptop if your "transferring" that license. According to the EULA anyway.

gplea said:

It's an ASUS ... it only has a Windows10 sticker on the back. It doesn't have any details like Retail/OEM. I bought it thru a retailer.

If this Asus was supplied with Windows 10 preinstalled then it has an OEM windows 10 key embedded in its bios firmware. If you do a clean install on the Asus, setup will read this to determine the edition to install and use it to activate Windows. You can check that it has a key, and for which edition, by running ShowKey Plus. However, I doubt you'll be able to use this OEM key to install on anything other than the Asus.

ShowKeyPlus - Windows 10 Forums

What Bree said. With the OEM embedded keys, they don't bother putting a product key on the COA sticker. No need to, you can't lose it and Windows detects and reads it automatically. OEM is only really transferable if say you had to replace your motherboard on "that" PC. They would give you a new license for that same PC. My ASUS laptops Windows 8 Core COA just says Windows 8 with no key listed. It makes it easy on the OEM's, they can just mass produce one generic COA sticker.

I would upgrade from Win 7 Pro to Win 10 Pro then if that activates you can do a Clean install of Win 10 if you want.