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sage: assume(x,'real')
sage: solve(exp(x)+exp(-1/2x) solve(exp(x)+exp(-1/2*x) == 2,x)
[x == 2log(1/2*sqrt(5) 2*log(1/2*sqrt(5) - 1/2), x == 0]

that ist ok!

how can i get here the solution x==0? x==0?

sage: solve(exp(x)+exp(1/2x) solve(exp(x)+exp(1/2*x) == 2,x)
[e^x == -e^(1/2x) -e^(1/2*x) + 2]
2]

Thanks for help.