There are things a GM can prepare in advance to help exude Intelligence, other than jumping into spontaneous role-playing
I live off of high-intelligence BBEGs like wizards who are as evil as they are ingenious. For what it's worth, here's what I have done at my table, and it gets me by (but note that much of this is not specific to a Solar, rather just any high-intelligence creature or NPC):
Look up some brainy "buzzwords" ahead of time that are relevant to your scenario. These days it's easy with an online thesaurus to get a list of smarty-pants words that fit your scenario, and have them ready so that you can word-bomb as you go along. Words like: pinnacle, impetus, quintessential, jocular, pulchritudinous, disinclined, indisposed, edification, explicate, perambulate. (Make sure you actually know what they mean and can use them correctly). Because you're the GM, you can know what some of the topics of conversation will have to be, and thus can prepare a specific list of relevant brainy-words. Really it just takes a few.
Work-up intricate traps and ploys ahead of time. Invest the time to create (or discover online) some really clever traps, cons, riddles, etc. that would require brains to create. Because you're the GM and you design the world, you can do this to enhance the seeming braininess of your character.
Describe props and preliminary scene action that support a smart-guy stereotype. Is the High-Int creature reading? Conducting experiments? Being asked its advice by nobles? All these things get across their Intelligence without you having to sound smart, but require you to be the GM who can insert these items/people in the picture.
Narrate, don't role-play. Instead of trying to sound smart, tell them that the character is sounding smart and just give it a little flavor. When I wanted to portray a genius wizard who had crafted his own modified Wand of Polymorph, I said: "He then jabbers on for ten minutes about things like 'the subject's readiness potential' and 'alternative embodiment' and 'the ontological structure of reality' until you are completely lost and have to ask him what practical difference there is when you use the wand." Again, because you're the GM, you can plan how to do this in advance, and it is more reliable than trying to "think on your feet" in spontaneous role-play.
I find that by combining at least two (or better, three) of the above I generally leave the players feeling they interacted with a genius.