Between Subjects Experimental Design- How to analyse

I have conducted an experiment with 2 conditions, 50 people in each condition. Each person completed a booklet of tasks and self-report measures (the same booklet in each condition).

I have conducted a simple T-test and have found significant differences between the two conditions on the outcome variable. HOW can I then look for potential mediators and moderators of this effect?!????

I have only ever been taught mediation/moderation in the context of multiple regression (Barron and kenny as far as I remember).

Any suggestions would be really helpful!

the tried and true regression should work perfectly. Just dummy variable a condition and add moderators to taste :).

What i mean by dummy variable is you have two conditions so in a regression, 1 will signify condition 1 and 0 as condition 2. Then you just add in whatever categorical or continuous variables you want to create your model.