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So its dependent on Is and Vt, great, we can either toast marshmallows on it orThere's a very precise relationship between emitter current Ie and Vbe:
Ie = Is * exp(Vbe/Vt)
Since Ic is about 99.5% of Ie for most small signal transistors (Ic = Ie * beta/(beta+1)), we often assume that:
Ic = Is * exp(Vbe/Vt)
Clearly we have, in a sense, a duty to let OPs know they are trying to workKlausST has explained circuit operation. OP didn't ask if it's a useful solution (not generally) and what are the conditions for correct operation (obviously some amount of load current).