With those restrictions, You probably can't.
Here is a similar question, the user was asking about 20 but without the restrictions.
Here is a search of how metropolitan subway colors are used.
Now let's see a process and see the results.
You need to start with a color wheel, which is not a color wheel but a color solid. In this case a cone.
Set up your restrictions. But as you want the same saturation, you only need the upper slice of the cone.
The lower layers are for brightness, but they also are reduced in saturation.
And now let's see what color we can have mechanically (D) and later with some adjustments to differentiate a bit more the mecanical selection.(E)
- "Light blue" (a lot of people do not know the term cyan)
- Turquoise? Sometimes is hard to differentiate it from cyan.
- Green (This fluorescent green is hard to differentiate from turquoise.
- Lime? Is this green or yellow?
- Yellow. But the apparent brightness is hard to combine with white text. Some subway systems fail to make this readable.
We have like 6 colors and some 3 possible colors without taking into account color-blind users.
Now let's see if we can expand this a bit removing the saturation (therefore brightness restriction)
We can move the green to a darker green, the Lime to a desaturated "grass" color, we can use brown, we can use gray and probably a marine blue, you can have a beige, some pastel purple...
As explained in the first link I provided, humans can not recognize that many colors, if they are not put together.
Also, there is a lot of differentiation per user.
Here is a funny image. http://www.thedoghousediaries.com/1406