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Here is its numerical solution for required values of parameters done with Maple:

a := .22: n := 5: mu := 3.18:
 fsolve(a = add(exp(-mu)*((mu-mu2)/mu2)^(k/2)*BesselI(k, 2*sqrt((mu-mu2)*mu2)), k = 1 .. n));

$2.002275629 $