Here is a very good video by Alphonso Gracia-Saz to prove that infinity minus infinity cannot be determined.

\infty - \infty \neq \infty

The best way to solve when you get an \infty - \infty is we try to rewrite it and manipulate it algebraically as shown below

https://www.youtube.com/watch?v=3EyFtXgJXTg&ab_channel=DKdemy

I found an answer from www.quora.com

What is infinity minus infinity? - Quora

Mathematical equations with infinity are not impossible to do. However, one must remember that infinity is not able to be exhausted. Because of this, there are ...

For more information, see What is infinity minus infinity? - Quora

I found an answer from math.stackexchange.com

calculus - What is the result of $\infty - \infty$? - Mathematics Stack ...

Aug 30, 2011 ... Perhaps an uninteresting way of speaking about infinity, but one you surely will understand, the first one I was ...... That's infinity minus infinity.

For more information, see calculus - What is the result of $\infty - \infty$? - Mathematics Stack ...

I found an answer from answers.yahoo.com

What's infinity minus infinity? | Yahoo Answers

At first, you may think that infinity subtracted from infinity is equal to zero. After all, any number subtracted by itself is equal to zero, however ...

For more information, see What's infinity minus infinity? | Yahoo Answers

I found an answer from en.wikipedia.org

Indeterminate form - Wikipedia

In calculus and other branches of mathematical analysis, limits involving an algebraic ... Note that zero to the power infinity is not an indeterminate form.

For more information, see Indeterminate form - Wikipedia

Infinity  - Infinity = indeterminate 

\infty - \infty =  indeterminate 

Example

Case 1:

= \lim_{x \to \infty} (2x -x)

= \lim_{x \to \infty} (2x) - \lim_{x \to \infty} (x)

= \infty - \infty   

= + \infty   

Case 2:

= \lim_{x \to \infty} (x - 2x)

= \lim_{x \to \infty} (x) - \lim_{x \to \infty} (2x)

= \infty - \infty

= - \infty

Case 3:

= \lim_{x \to \infty} (x - x)

= \infty - \infty

= 0

Hence, we can conclude that   \infty - \infty =  indeterminate. Because we have different responses ( + \infty,-\infty, \text{ and } 0 ) in each case, we are unable to figure out that this is the exact answer.