Hello and welcome, Michael ~
I'm not an expert (nor a doctor) but the shorthand explanation is that the noise -'tinnitus' - originates in your brain, not your ears, although some cochlea damage is often present in tinnitus sufferers. Not all acoustic neuroma patients experience tinnitus but the majority do. However, the level of intensity varies from person to person. I have tinnitus but it is relatively mild and does not negatively impact my life. Others suffer with very 'loud' and disturbing tinnitus. The level of intensity often varies according to your state of rest, physical activity, etc.
Unfortunately, to date, there is no known, scientifically-proven 'cure' for tinnitus - although homeopathic remedies abound. Some actually work but usually in a very random fashion. Homeopathic remedies for tinnitus are not FDA approved and so I would caution anyone intending to try them not to set your expectations too high. However, if anyone ever does discover a scientifically-proven remedy for all levels of tinnitus, they'll be an instant millionaire.