In terms of Ic you have this formula: Ic = Ib * B
where B = beta and Ib = base current.
In terms of Ie you have this formula: Ie = Ib + Ic
where Ic = collector current and Ie = emitter current
If the 1st equation is substituted to the 2nd equation in terms of Ic you will have this equation Ie = (Ic/B) + Ic
Extracting Ic you will have this equation Ie = Ic((1/B) + 1)
Typically B = 100 so ((1/B) + 1) is approximately equal to 1