This is not a tutorial on how to play solo guitar, but rather things to be aware of when playing, when you keep the following in mind, then you'll know how to get the sound you want.
The main thing to remember is that you are in control of everything. When we play with a backing track the rhythm and the bass is usually accounted for but when it's just us then if we want these things again, we have to do it.
The main 3 voices are the bass, mid and treble. We don't need to have all voices going at once, but to create rich harmony it will be useful to have always at least one bass and mid note occuring when we play. Additionally with the bass voice you can imitate bass lines.
By now we should already know how to control the mids from our chords, but they are the essence of the guitar, so this represents our chords or just guitar itself.
The treble pierces through the mid and the bass and so that's where we can put melodies so that they're heard clearly.
By using the properities of the three voices to our advantage we can get a full sound just from one guitar.
Rhythm is also very important, since there is no one keeping time like a drummer, drum machine or metronome, then you will have to provide the rhythm.
This is a challenge since you're already thinking about the three voices and making that sound good, but at least you should have some sort of stead pulse on the bass and possibly mids.
A great example of someone who can pull of rhythm in solo guitar is Chet Atkins.