You won't be able to check an exact inequality since it is a continuous random variable, but what you can do is check an interval.
So basically you want to find whether the difference lies in a particular interval of [-e,e] for some small e > 0.
You can find the sum of two variables distribution by using convolution.
List of convolutions of probability distributions - Wikipedia, the free encyclopedia
we can see that the distribution will be a gamma however this is only for summing random variables. Yheoutiou will need to find the PDF of the -X where X is exponential and then use the convolution theorem to get the PDF.
Once you have the PDF then just calculate the probability in [-e,e]