Don't panic! It can take any cat MONTHS to adjust to new pets, even a new kitten. Here is what I suggest:
Setup a bathroom to house the new kitten in for just one week. Provide litter box, food, water, some comfort toys, and something that makes soft noise to keep him/her comfortable.
This does two things for you at once: First, it will help you establish how your kitten uses the litter box and that there will be no future accidents, and Second, your older can can smell the kittens scent through the crack under the door. They can check each other out without actually seeing each other and freaking out.
Expect hissing and growling from either party, it's normal. After 7 days, allow the new kitten some freedom. After 2 weeks, move the litter box to the same room your other box is setup in (and grab the kitten while you are at it and show him/her where it is). After a few days, you can either get rid of the extra litter box or keep it, up to you.
Don't worry about the cats adjusting to each other. You will get hissing,growling, and an occasional pop of the paws from one cat to the other. NORMAL cat behavior. DONT FORCE them TOGETHER. Just let them work it out for themselves.
It's 10 times easier for an older cat to adjust to kittens verses another older cat. The kitten will adjust real fast, even maybe within days.
I do kitten/cat fostering all the time and I have my own set of kitties, so it works every time with me.