Can I add a 2tb hard drive to my optiplex 7010

Depends on which 7010 you have, in terms of what you need and what it'll cost. The USFF ones from this period are usually only able to take one drive, and it has to be 2.5” (slightly more expensive). The standard SFF ones usually take 1-2 3.5” drives, if the chassis is large enough otherwise it might accept 1 3.5” drive, or 2 2.5” ones depending on the model. The full desktop has no problems taking 2 3.5” drives, and you can use your old one as a secondary drive without an issue.

The longstanding one which isn't as obvious is Dell's USFF and the BIOS's dependency on there being a HD fan. While newer ones aren't as picky (read: widespread SSD era) and others will throw a POST nag up until you find the fan and you CANNOT BYPASS it. Generally speaking, if it lacks the M.2 slot, it will probably nag; M.2 units might for the 2.5" bay if it's a spinner but not a SATA SSD, so see what happens. The issue is Dell may not have installed the caddy and cabling you need, so you need to add it. I'd try and get part numbers if possible, so you know what's required. EVEN IF THE DRIVE CAN FOREGO IT LIKE AN SSD, THE NAGGY DELLS DO NOT CARE. Spinning drives genuinely need this fan. The reason it is so hard to know how critical that fan is comes down to Dell using the HD fan error on some tower desktops which do not have a header for a bad rear fan. If you ever see it, try seeing if the unit has any secondary cooling; if it does, clean the fan out first. If it remains, you need a new one. And if it persists, it requires the HD fan.

For the full desktop system, this is the caddy you need if you keep your original 1TB HD as a secondary drive:

You can get these for $5-10 a caddy all day with how many systems use them. Sometimes less if the seller wants to get rid of them. USFF units may need a little more research.