Color coded lines can work wonders. The trick with that is that the colors need to be different enough in shade to tell apart, but should still look good. Unless you want to burn people's eyes out. This is also good, because colors usually have a sort of "sound" to them. This probably sounds weird. But if you try coloring some text and read it in your head, purple will be a "deeper voice". Hard to explain.
Alternatively you can color the text depending on what is a dominant color on a character. Since the characters here are the duo from Kindread (at least that's what I assume), both have red hair. The older one, since older could have a darker shade of red as a color, while the younger girl can have a more vibrant red shade.
Other than that you could just put who is talking in front of each line, but that's not really a good idea, because it breaks immersion even more than putting "she said" after.
Speaking of "she said"... If you grab any half-way decent book, even those have these at the end of certain lines. These are there to specify who is speaking when it's not obvious, because said line could come from multiple characters in the scene. But that topic comes down to writing skills.
Other than that you can specify the speaker by describing their current state a bit.
I'll put an example in the spoiler below from the demo:
PS: I've written the whole 2nd paragraph, then I realised this is a test, so I assume it didn't get too much effort in all... I'll just keep it there though. Maybe it's helpful in a way?