I have an older bike with a blown tube. I don't have the money to replace the tire but I have the tube. The tire is quite old probably at least ten years old since that is when the last owner bought the bike. Is there a way to remove the tire without wrecking it or am I going to have to wait till I can afforded a new tire.
If the tyre's safe to ride on, removing and replacing it shouldn't damage it, as long as you use the correct tools. These are tyre levers, which can be bought for literally a couple of dollars/euros/pounds. The internet will tell you how to do this; it's not difficult.
If the tyre can't be removed without damaging it, then it's not safe to ride.
Tires are designed to be removable from rims and re-installed. For instance, to replace or repair a blown inner tube.
If the tire is a little old, you may have to exercise a little more caution. There are many video tutorials available to show you what the proper tools are, and how to remove the tire, remove and replace the tube and replace the tire properly.
Here's a good one: https://www.parktool.com/blog/repair-help/tire-and-tube-removal-and-installation.