I would likewise expect the engine numbers to be on the cowling tinwork as is the norm'..they will be actually stamped into the tinwork. They are often quite hard to read on older machines if either some rusting has occured or if a thick coat of paint has been added...but they will be there.
The only time when they will be missing is if a new cowling has been fitted...these spares cowlings came in plain grey primer rather than original engine colour and then had a foil sticker to scribe numbers into...or things can get blurred if a cowling from another engine has been fitted..then of course it will have numbers ..but the wrong ones.!!
...on some I think the numbers were on the vertical side of the tinwork on the side facing the carb.
They will be in 3 sections Model, Type, Code
Once you have tracked them down they are the key to everything. You can download an operators manual from www.briggsandstratton.com
and also the full engine parts list..the very same one that a machinery agent will have.
They even provide the date of manufacture of the engine....the last set, Code, read year/month/day/factory.
Your model of Titan is within the last design style of UK Merry Tiller...these came out in c.1983 and I have a reference to them finishing in 1989??. Titan seems to be listed as AC3484 up to about 1986 then seems to change to W25021.
Out of curiosity the last price ref I have for this Titan model is in July 1989 when it was shown as £895 inc' vat.
If you visit this site; http://merrytiller.dyndns.org/
there are some parts diagrams and operating manual some of which suit your Titan model. Look under the Major link at the top of the page as these are the ones for your design type. The Titan shown lower down the page is for a previous use of the Titan name..in the same way as car manufacturers re use model names.
..I had a rummage and found a brochure which I think may be from 1984 and by chance it does list an engine model type which was used then..Model 131232.
However do track down the actual numbers from your engine to ensure getting The correct parts.
All the best,