Lighting, Light Fixtures, Ceiling and Exhaust Fans - replace old bthrm light/mirror w/ sconce and outlet

Hi, I could really use some help here. My home and bathroom are both about 40 years old (just bought the house). In the bathroom is an old vanity mirror/light unit that I would like to replace with a wall sconce operated by a switch, I would also like to add an outlet to use for a hairdryer, etc. (currently there is no outlet in the bathroom). FYI there is an overhead light operated by a switch at the door , but likely unrelated to this challenge.

Here is where I am at the moment. I have removed the vanity/light unit and disconnected the electrical wires. I now have the opening in the wall (which I will patch) and two wires (a white and a black) coming out of the electrical casing. There is no junction box at all.

Is this possible? Can both things be wired from the same two existing wires? Let me know if you need more information. I really appreciate any guidance you can provide.

Unfortunately, to add a receptacle requires you to conform to today's electrical codes. And today's electrical codes almost certainly will not allow you to add a receptacle to this circuit. You need a new 20-amp circuit for your receptacle.

Furthermore, you absolutely may not patch the wall over live electrical connections. All splices must be in permanently accessible junction boxes.