This question has received a number of good responses already and I see that one has already been checked as the best one, but I recently did a study on a list of 2,000 of the most frequent nouns in Spanish (which I subsequently whittled down to 1,800). I compiled it to answer this question:
What percentage of nouns ending in -a are masculine and what percentage of nouns ending in -o are feminine?
but in the process compiled data that may add insight to your inquiry. I can't say that what I'm about to add definitively answers your question because, for starters, I didn't look at every noun in the Spanish lexicon, but you may find it interesting, nonetheless.
First of all, I grouped these nouns into two main categories -- those that have both biological and grammatical gender (e.g., "chico") and those that have just grammatical gender (e.g., "año"). I didn't set out to study nouns that ended in -e, but thought it would be good to have a category for nouns that ended in a vowel other than -a or -o. What I discovered, among nouns with just grammatical gender, is that 97 percent of the time, if a noun does not end in -a or -o, that vowel ending is going to be -e. Only 5 words in this set of nouns ended in a vowel other than -e ("ley," "taxi," "espiritú," "menú," and "whisky").
However, to more directly answer your question:
Are the majority of words ending in e masculine or feminine?
it appears that nouns that end in -e are almost three times as likely to be masculine as they are to be feminine. I don't know how much this will help you since nouns ending in -e only appear to comprise 10 percent of nouns (across all categories -- those taking both biological and grammatical gender and those with just grammatical gender). But, if you do encounter one and need to guess, it appears that guessing that it is masculine is a good bet.
The other thing that really jumped out at me from this study of nouns appeared in the category I'll call "epicene nouns," which, linguistically, means the noun form does not change for male or female biological gender. Spanish refers to these types of nouns as "common gender" (género común) nouns. Guifa, a top contributor to this StackExchange, makes reference to this in the thread, "Origin of gender-neutral nouns ...” Examples of this include "artista," "turista," and "estudiante." For more examples, visit "Double-gendered nouns with equivalent meaning (género común)." Male and female are identified by the inclusion of an article (e.g., "el artista" for a male artist and "la artista" for a female artist) or descriptive adjective (e.g., "artista talentoso" would be referring to a male artist). What was surprising to me about this category was how many of these types of words end in neither -a (only 35%) nor -o (only 15%), but -e (63%). Then again, with so many nouns ending in -a being of feminine gender and so many of those ending in -o being of masculine, perhaps the letter -e is something of a logical choice for gender neutrality in noun forms. In other words, it should have actually seemed more surprising if the majority of these ended in -a or -o since the noun itself applies to both male and female.
EDIT: I learned even later that epicene nouns are NOT the same as common gender nouns. Please see guifa's comment below for clarification. For the record, my study lumped both epicene nouns and common gender nouns together, but I believe only two were true epicenes -- "la víctima" and "el miembro." I am not certain whether or not "el bebé" and "la mascota" are also considered epicene nouns. I am assuming "la persona" is another of these epicene nouns, but I scrubbed it from the list, uncertain of which category it should belong to. Does anyone reading this know of a good, comprehensive listing of epicene nouns? I think this would be immensely helpful to a student trying to go from the beginning level to the intermediate or advanced.