Ethoxyethane and 1-methoxypropane are

Metamers are those isomers in which the number of alkyl groups on the both sides of the functional group is different.

Ethoxyethane:

${\mathrm{CH}}_3-{\mathrm{CH}}_2-\mathrm{O}-{\mathrm{CH}}_2-{\mathrm{CH}}_3$

1-methoxypropane:

${\mathrm{CH}}_3-\mathrm{CO}-{\mathrm{CH}}_2-{\mathrm{CH}}_2-{\mathrm{CH}}_3$

Different alkyl groups present on either sides of O atoms, hence they are metamers.