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You need to define the variables using the var command. Also, the syntax for solve is slightly different.

var('a k n m')
solve([a*exp(k*2) - n==0, a*exp(k*8)-m==0], [a, k], solution_dict=True)

Unfortunately, Sage (which uses Maxima for this) does not solve the equation.

However, sympy does a nice job of solving here.

var('a k n m')
import sympy as sp
sp.solve([a*exp(k*2) - n, a*exp(k*8)-m], [a, k],dict=True)