Brake pedal stopped working after accidentally driving with e brake on for about >10 min around 60 mph?

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First, there's no "E brake" on any vehicle. There is a parking brake that you are supposed to set when you park the vehicle even if it is an automatic transmission most importantly if you are parked on a grade or slope. 

No parking brake can be used as an "emergency brake" to stop a vehicle, it simply wasn't designed for that and is totally inadequate for such a purpose.

You may have burned up what was left of the parking brake shoes, also, when you reach the boiling point of the brake fluid you will have bubbles in the brake line and or brake caliper and or brake cylinders. You'll have to have the brakes inspected and have the fluid bled out of the system to get the air out.  

Your e-brake cables are seized in their housing. You likely have a brake fluid leak and the brake fluid was burning on the exhaust pipes. The e-brake didn't cause the brake pedal to go down. Put the car up on a lift and check all the brake lines for leakage.

You smoked your brakes. Get them inspected ASAP.

So, you probably badly overheated the rear brakes and the seals in the rear brake cylinders probably failed. 

You have worn out your rear brake pads. Time to have new brakes pads and more than likely new rotors installed on the rear of your vehicle.��