"Every" can be used without any limits, whereas "each" can only be used when referring to a specific or limited set, however large.
For example, you might say "every child should have an education" which would be a blanket statement about all children, everywhere - even those not yet born. It is (sadly) not true to say that every child does receive an education. However, if you were talking about a specific set of children that you know were educated, you could say of that set "each child received an education".
Likewise with your example, if emitting radiation is true of all solar eruptions - even ones that have not been observed, and in stars that have not been discovered - and your intention is to make a blanket statement about solar eruptions then you should use 'every'. But, if you were speaking about the results of a series of observations of solar eruptions, either in one star or among many, you could refer to 'each of them', meaning each of the eruptions you observed.